LMFDB - Embedded newform 72.4.l.b.11.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,4,Mod(11,72)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("72.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$72 = 2^{3} \cdot 3^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	72.l (of order $6$ , degree $2$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.24813752041$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.31
Character	$\chi$	$=$	72.11
Dual form			72.4.l.b.59.31

$q$ -expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.82386 + 0.160583i) q^{2} +(-5.18814 - 0.288534i) q^{3} +(7.94843 + 0.906929i) q^{4} +(5.34568 + 9.25900i) q^{5} +(-14.6043 - 1.64791i) q^{6} +(15.5169 + 8.95867i) q^{7} +(22.2996 + 3.83743i) q^{8} +(26.8335 + 2.99391i) q^{9} +(13.6087 + 27.0046i) q^{10} +(-19.0639 - 11.0065i) q^{11} +(-40.9758 - 6.99866i) q^{12} +(17.9061 - 10.3381i) q^{13} +(42.3789 + 27.7898i) q^{14} +(-25.0626 - 49.5793i) q^{15} +(62.3550 + 14.4173i) q^{16} +36.2107i q^{17} +(75.2934 + 12.7634i) q^{18} -125.564 q^{19} +(34.0925 + 78.4426i) q^{20} +(-77.9188 - 50.9559i) q^{21} +(-52.0663 - 34.1423i) q^{22} +(-88.1103 - 152.612i) q^{23} +(-114.586 - 26.3433i) q^{24} +(5.34734 - 9.26186i) q^{25} +(52.2246 - 26.3180i) q^{26} +(-138.352 - 23.2752i) q^{27} +(115.210 + 85.2800i) q^{28} +(-77.3286 + 133.937i) q^{29} +(-62.8118 - 144.030i) q^{30} +(243.700 - 140.701i) q^{31} +(173.767 + 50.7257i) q^{32} +(95.7301 + 62.6039i) q^{33} +(-5.81483 + 102.254i) q^{34} +191.561i q^{35} +(210.569 + 48.1329i) q^{36} -223.656i q^{37} +(-354.576 - 20.1634i) q^{38} +(-95.8823 + 48.4690i) q^{39} +(83.6761 + 226.986i) q^{40} +(47.3067 - 27.3125i) q^{41} +(-211.849 - 156.405i) q^{42} +(157.422 - 272.663i) q^{43} +(-141.545 - 104.774i) q^{44} +(115.723 + 264.456i) q^{45} +(-224.305 - 445.103i) q^{46} +(-230.270 + 398.839i) q^{47} +(-319.346 - 92.7905i) q^{48} +(-10.9844 - 19.0256i) q^{49} +(16.5874 - 25.2955i) q^{50} +(10.4480 - 187.866i) q^{51} +(151.701 - 65.9321i) q^{52} -158.027 q^{53} +(-386.950 - 87.9430i) q^{54} -235.349i q^{55} +(311.643 + 259.320i) q^{56} +(651.443 + 36.2295i) q^{57} +(-239.874 + 365.803i) q^{58} +(-403.976 + 233.236i) q^{59} +(-154.243 - 416.808i) q^{60} +(382.288 + 220.714i) q^{61} +(710.771 - 358.185i) q^{62} +(389.550 + 286.849i) q^{63} +(482.548 + 171.146i) q^{64} +(191.441 + 110.529i) q^{65} +(260.276 + 192.158i) q^{66} +(-193.518 - 335.182i) q^{67} +(-32.8406 + 287.818i) q^{68} +(413.095 + 817.192i) q^{69} +(-30.7614 + 540.942i) q^{70} -20.3800 q^{71} +(586.889 + 169.735i) q^{72} -370.437 q^{73} +(35.9154 - 631.576i) q^{74} +(-30.4151 + 46.5089i) q^{75} +(-998.036 - 113.878i) q^{76} +(-197.208 - 341.574i) q^{77} +(-278.542 + 121.473i) q^{78} +(562.808 + 324.937i) q^{79} +(199.840 + 654.415i) q^{80} +(711.073 + 160.674i) q^{81} +(137.974 - 69.5302i) q^{82} +(516.463 + 298.180i) q^{83} +(-573.118 - 475.686i) q^{84} +(-335.275 + 193.571i) q^{85} +(488.324 - 744.685i) q^{86} +(439.837 - 672.572i) q^{87} +(-382.880 - 318.598i) q^{88} -1210.30i q^{89} +(284.318 + 765.370i) q^{90} +370.463 q^{91} +(-561.931 - 1292.93i) q^{92} +(-1304.95 + 659.657i) q^{93} +(-714.297 + 1089.29i) q^{94} +(-671.225 - 1162.60i) q^{95} +(-886.890 - 313.309i) q^{96} +(-794.702 + 1376.46i) q^{97} +(-27.9634 - 55.4897i) q^{98} +(-478.597 - 352.419i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$64 q - 3 q^{2} + 6 q^{3} - 17 q^{4} - 3 q^{6} + 42 q^{9} + 12 q^{10} + 48 q^{11} + 318 q^{12} + 72 q^{14} + 127 q^{16} + 330 q^{18} - 220 q^{19} - 234 q^{20} - 217 q^{22} + 189 q^{24} - 902 q^{25} - 252 q^{27}+ \cdots - 2118 q^{99}+O(q^{100})$ 64 * q - 3 * q^2 + 6 * q^3 - 17 * q^4 - 3 * q^6 + 42 * q^9 + 12 * q^10 + 48 * q^11 + 318 * q^12 + 72 * q^14 + 127 * q^16 + 330 * q^18 - 220 * q^19 - 234 * q^20 - 217 * q^22 + 189 * q^24 - 902 * q^25 - 252 * q^27 - 132 * q^28 + 420 * q^30 - 693 * q^32 - 660 * q^33 + 509 * q^34 - 537 * q^36 - 1977 * q^38 - 36 * q^40 + 1620 * q^41 + 72 * q^42 - 292 * q^43 + 48 * q^46 + 765 * q^48 + 1762 * q^49 - 1227 * q^50 - 1794 * q^51 + 330 * q^52 - 645 * q^54 + 942 * q^56 - 294 * q^57 - 282 * q^58 + 5592 * q^59 + 1236 * q^60 + 1090 * q^64 - 6 * q^65 + 3522 * q^66 + 68 * q^67 - 2025 * q^68 + 600 * q^70 + 1875 * q^72 - 868 * q^73 - 420 * q^74 - 4254 * q^75 - 1471 * q^76 + 3228 * q^78 + 498 * q^81 + 362 * q^82 + 3654 * q^83 - 2028 * q^84 - 4119 * q^86 + 3155 * q^88 + 2958 * q^90 - 1380 * q^91 - 744 * q^92 - 138 * q^94 - 4782 * q^96 - 1912 * q^97 - 2118 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$ .

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	2.82386	+	0.160583i	0.998387	+	0.0567746i
$2$	2.82386	+	0.160583i	0.998387	+	0.0567746i
$3$	−5.18814	−	0.288534i	−0.998457	−	0.0555285i
$3$	−5.18814	−	0.288534i	−0.998457	−	0.0555285i
$4$	7.94843	+	0.906929i	0.993553	+	0.113366i
$5$	5.34568	+	9.25900i	0.478132	+	0.828150i	0.999686	−	0.0250690i	$-0.00798055\pi$
$5$	5.34568	+	9.25900i	0.478132	+	0.828150i	−0.521553	+	0.853219i	$0.674647\pi$
$6$	−14.6043	−	1.64791i	−0.993694	−	0.112126i
$7$	15.5169	+	8.95867i	0.837832	+	0.483723i	0.856527	−	0.516103i	$-0.172618\pi$
$7$	15.5169	+	8.95867i	0.837832	+	0.483723i	−0.0186945	+	0.999825i	$0.505951\pi$
$8$	22.2996	+	3.83743i	0.985514	+	0.169592i
$9$	26.8335	+	2.99391i	0.993833	+	0.110886i
$10$	13.6087	+	27.0046i	0.430343	+	0.853960i
$11$	−19.0639	−	11.0065i	−0.522543	−	0.301690i	0.215432	−	0.976519i	$-0.430884\pi$
$11$	−19.0639	−	11.0065i	−0.522543	−	0.301690i	−0.737974	+	0.674829i	$0.764217\pi$
$12$	−40.9758	−	6.99866i	−0.985725	−	0.168362i
$13$	17.9061	−	10.3381i	0.382021	−	0.220560i	−0.296676	−	0.954978i	$-0.595878\pi$
$13$	17.9061	−	10.3381i	0.382021	−	0.220560i	0.678697	+	0.734418i	$0.262545\pi$
$14$	42.3789	+	27.7898i	0.809018	+	0.530510i
$15$	−25.0626	−	49.5793i	−0.431409	−	0.853422i
$16$	62.3550	+	14.4173i	0.974296	+	0.225271i
$17$			36.2107i			0.516611i	0.966063	+	0.258306i	$0.0831642\pi$
$17$			36.2107i			0.516611i	−0.966063	+	0.258306i	$0.916836\pi$
$18$	75.2934	+	12.7634i	0.985935	+	0.167131i
$19$	−125.564			−1.51612			−0.758062	−	0.652182i	$-0.773854\pi$
$19$	−125.564			−1.51612			−0.758062	+	0.652182i	$0.773854\pi$
$20$	34.0925	+	78.4426i	0.381166	+	0.877015i
$21$	−77.9188	−	50.9559i	−0.809679	−	0.529500i
$22$	−52.0663	−	34.1423i	−0.504571	−	0.330871i
$23$	−88.1103	−	152.612i	−0.798794	−	1.38355i	−0.920402	−	0.390974i	$-0.872138\pi$
$23$	−88.1103	−	152.612i	−0.798794	−	1.38355i	0.121607	−	0.992578i	$-0.461195\pi$
$24$	−114.586	−	26.3433i	−0.974577	−	0.224054i
$25$	5.34734	−	9.26186i	0.0427787	−	0.0740949i
$26$	52.2246	−	26.3180i	0.393927	−	0.198515i
$27$	−138.352	−	23.2752i	−0.986142	−	0.165900i
$28$	115.210	+	85.2800i	0.777593	+	0.575586i
$29$	−77.3286	+	133.937i	−0.495157	+	0.857638i	−0.999984	−	0.00558276i	$-0.998223\pi$
$29$	−77.3286	+	133.937i	−0.495157	+	0.857638i	0.504827	+	0.863221i	$0.331556\pi$
$30$	−62.8118	−	144.030i	−0.382260	−	0.876538i
$31$	243.700	−	140.701i	1.41193	−	0.815179i	0.416362	−	0.909199i	$-0.363305\pi$
$31$	243.700	−	140.701i	1.41193	−	0.815179i	0.995570	+	0.0940195i	$0.0299716\pi$
$32$	173.767	+	50.7257i	0.959935	+	0.280222i
$33$	95.7301	+	62.6039i	0.504984	+	0.330241i
$34$	−5.81483	+	102.254i	−0.0293304	+	0.515778i
$35$			191.561i			0.925134i
$36$	210.569	+	48.1329i	0.974856	+	0.222838i
$37$		−	223.656i		−	0.993754i	−0.867821	−	0.496877i	$-0.834480\pi$
$37$		−	223.656i		−	0.993754i	0.867821	−	0.496877i	$-0.165520\pi$
$38$	−354.576	−	20.1634i	−1.51368	−	0.0860774i
$39$	−95.8823	+	48.4690i	−0.393678	+	0.199006i
$40$	83.6761	+	226.986i	0.330759	+	0.897241i
$41$	47.3067	−	27.3125i	0.180197	−	0.104037i	−0.407188	−	0.913344i	$-0.633491\pi$
$41$	47.3067	−	27.3125i	0.180197	−	0.104037i	0.587385	+	0.809308i	$0.300157\pi$
$42$	−211.849	−	156.405i	−0.778311	−	0.574615i
$43$	157.422	−	272.663i	0.558294	−	0.966994i	−0.439345	−	0.898319i	$-0.644789\pi$
$43$	157.422	−	272.663i	0.558294	−	0.966994i	0.997639	−	0.0686756i	$-0.0218774\pi$
$44$	−141.545	−	104.774i	−0.484972	−	0.358984i
$45$	115.723	+	264.456i	0.383354	+	0.876061i
$46$	−224.305	−	445.103i	−0.718955	−	1.42667i
$47$	−230.270	+	398.839i	−0.714644	+	1.23780i	0.248453	+	0.968644i	$0.420078\pi$
$47$	−230.270	+	398.839i	−0.714644	+	1.23780i	−0.963097	+	0.269156i	$0.913255\pi$
$48$	−319.346	−	92.7905i	−0.960284	−	0.279024i
$49$	−10.9844	−	19.0256i	−0.0320246	−	0.0554683i
$50$	16.5874	−	25.2955i	0.0469164	−	0.0715466i
$51$	10.4480	−	187.866i	0.0286866	−	0.515814i
$52$	151.701	−	65.9321i	0.404562	−	0.175830i
$53$	−158.027			−0.409560			−0.204780	−	0.978808i	$-0.565648\pi$
$53$	−158.027			−0.409560			−0.204780	+	0.978808i	$0.565648\pi$
$54$	−386.950	−	87.9430i	−0.975133	−	0.221621i
$55$		−	235.349i		−	0.576991i
$56$	311.643	+	259.320i	0.743660	+	0.618805i
$57$	651.443	+	36.2295i	1.51379	+	0.0841880i
$58$	−239.874	+	365.803i	−0.543051	+	0.828142i
$59$	−403.976	+	233.236i	−0.891410	+	0.514656i	−0.874403	−	0.485200i	$-0.838747\pi$
$59$	−403.976	+	233.236i	−0.891410	+	0.514656i	−0.0170066	+	0.999855i	$0.505414\pi$
$60$	−154.243	−	416.808i	−0.331879	−	0.896827i
$61$	382.288	+	220.714i	0.802409	+	0.463271i	0.844313	−	0.535851i	$-0.180009\pi$
$61$	382.288	+	220.714i	0.802409	+	0.463271i	−0.0419039	+	0.999122i	$0.513342\pi$
$62$	710.771	−	358.185i	1.45594	−	0.733703i
$63$	389.550	+	286.849i	0.779028	+	0.573643i
$64$	482.548	+	171.146i	0.942477	+	0.334270i
$65$	191.441	+	110.529i	0.365313	+	0.210913i
$66$	260.276	+	192.158i	0.485420	+	0.358378i
$67$	−193.518	−	335.182i	−0.352865	−	0.611180i	0.633885	−	0.773427i	$-0.281459\pi$
$67$	−193.518	−	335.182i	−0.352865	−	0.611180i	−0.986750	+	0.162247i	$0.948126\pi$
$68$	−32.8406	+	287.818i	−0.0585662	+	0.513281i
$69$	413.095	+	817.192i	0.720735	+	1.42577i
$70$	−30.7614	+	540.942i	−0.0525242	+	0.923642i
$71$	−20.3800			−0.0340657			−0.0170328	−	0.999855i	$-0.505422\pi$
$71$	−20.3800			−0.0340657			−0.0170328	+	0.999855i	$0.505422\pi$
$72$	586.889	+	169.735i	0.960632	+	0.277825i
$73$	−370.437			−0.593922			−0.296961	−	0.954890i	$-0.595973\pi$
$73$	−370.437			−0.593922			−0.296961	+	0.954890i	$0.595973\pi$
$74$	35.9154	−	631.576i	0.0564200	−	0.992151i
$75$	−30.4151	+	46.5089i	−0.0468271	+	0.0716051i
$76$	−998.036	−	113.878i	−1.50635	−	0.171877i
$77$	−197.208	−	341.574i	−0.291869	−	0.505531i
$78$	−278.542	+	121.473i	−0.404342	+	0.176334i
$79$	562.808	+	324.937i	0.801530	+	0.462763i	0.844006	−	0.536334i	$-0.180191\pi$
$79$	562.808	+	324.937i	0.801530	+	0.462763i	−0.0424761	+	0.999097i	$0.513525\pi$
$80$	199.840	+	654.415i	0.279285	+	0.914572i
$81$	711.073	+	160.674i	0.975409	+	0.220403i
$82$	137.974	−	69.5302i	0.185813	−	0.0936382i
$83$	516.463	+	298.180i	0.683002	+	0.394331i	0.800985	−	0.598684i	$-0.204310\pi$
$83$	516.463	+	298.180i	0.683002	+	0.394331i	−0.117983	+	0.993016i	$0.537643\pi$
$84$	−573.118	−	475.686i	−0.744432	−	0.617877i
$85$	−335.275	+	193.571i	−0.427832	+	0.247009i
$86$	488.324	−	744.685i	0.612295	−	0.933738i
$87$	439.837	−	672.572i	0.542017	−	0.828819i
$88$	−382.880	−	318.598i	−0.463809	−	0.385939i
$89$		−	1210.30i		−	1.44148i	−0.693206	−	0.720739i	$-0.743803\pi$
$89$		−	1210.30i		−	1.44148i	0.693206	−	0.720739i	$-0.256197\pi$
$90$	284.318	+	765.370i	0.332998	+	0.896412i
$91$	370.463			0.426759
$92$	−561.931	−	1292.93i	−0.636797	−	1.46519i
$93$	−1304.95	+	659.657i	−1.45502	+	0.735519i
$94$	−714.297	+	1089.29i	−0.783767	+	1.19523i
$95$	−671.225	−	1162.60i	−0.724908	−	1.25558i
$96$	−886.890	−	313.309i	−0.942894	−	0.333094i
$97$	−794.702	+	1376.46i	−0.831853	+	1.44081i	0.0647144	+	0.997904i	$0.479386\pi$
$97$	−794.702	+	1376.46i	−0.831853	+	1.44081i	−0.896567	+	0.442908i	$0.853947\pi$
$98$	−27.9634	−	55.4897i	−0.0288238	−	0.0571970i
$99$	−478.597	−	352.419i	−0.485867	−	0.357772i
$100$	50.9027	−	68.7675i	0.0509027	−	0.0687675i
$101$	636.447	−	1102.36i	0.627018	−	1.08603i	−0.361129	−	0.932516i	$-0.617609\pi$
$101$	636.447	−	1102.36i	0.627018	−	1.08603i	0.988147	−	0.153511i	$-0.0490580\pi$
$102$	59.6720	−	528.831i	0.0579255	−	0.513354i
$103$	−1190.34	+	687.241i	−1.13871	+	0.657436i	−0.946111	−	0.323841i	$-0.895026\pi$
$103$	−1190.34	+	687.241i	−1.13871	+	0.657436i	−0.192601	+	0.981277i	$0.561692\pi$
$104$	438.972	−	161.823i	0.413892	−	0.152577i
$105$	55.2719	−	993.844i	0.0513713	−	0.923707i
$106$	−446.246	−	25.3764i	−0.408899	−	0.0232526i
$107$			1612.72i			1.45708i	0.685004	+	0.728540i	$0.259801\pi$
$107$			1612.72i			1.45708i	−0.685004	+	0.728540i	$0.740199\pi$
$108$	−1078.57	−	310.477i	−0.960978	−	0.276626i
$109$		−	1546.65i		−	1.35911i	−0.733626	−	0.679554i	$-0.762174\pi$
$109$		−	1546.65i		−	1.35911i	0.733626	−	0.679554i	$-0.237826\pi$
$110$	37.7931	−	664.595i	0.0327585	−	0.576061i
$111$	−64.5326	+	1160.36i	−0.0551816	+	0.992221i
$112$	838.394	+	782.329i	0.707328	+	0.660028i
$113$	−1193.12	+	688.848i	−0.993267	+	0.573463i	−0.906249	−	0.422744i	$-0.861067\pi$
$113$	−1193.12	+	688.848i	−0.993267	+	0.573463i	−0.0870178	+	0.996207i	$0.527734\pi$
$114$	1833.77	+	206.918i	1.50656	+	0.169997i
$115$	942.020	−	1631.63i	0.763859	−	1.32304i
$116$	−736.112	+	994.458i	−0.589192	+	0.795975i
$117$	511.435	−	223.798i	0.404122	−	0.176839i
$118$	−1178.23	+	593.754i	−0.919192	+	0.463216i
$119$	−324.400	+	561.877i	−0.249897	+	0.432834i
$120$	−368.630	−	1201.78i	−0.280426	−	0.914223i
$121$	−423.213	−	733.026i	−0.317966	−	0.550734i
$122$	1044.09	+	684.655i	0.774813	+	0.508080i
$123$	−253.314	+	128.051i	−0.185696	+	0.0938700i
$124$	2064.64	−	897.329i	1.49524	−	0.649859i
$125$	1450.76			1.03808
$126$	1053.97	+	872.577i	0.745203	+	0.616947i
$127$		−	266.075i		−	0.185908i	−0.995670	−	0.0929539i	$-0.970369\pi$
$127$		−	266.075i		−	0.185908i	0.995670	−	0.0929539i	$-0.0296309\pi$
$128$	1335.17	+	560.784i	0.921979	+	0.387240i
$129$	−895.400	+	1369.19i	−0.611129	+	0.934501i
$130$	522.855	+	342.860i	0.352749	+	0.231314i
$131$	284.037	−	163.989i	0.189438	−	0.109372i	−0.402281	−	0.915516i	$-0.631783\pi$
$131$	284.037	−	163.989i	0.189438	−	0.109372i	0.591720	+	0.806144i	$0.298449\pi$
$132$	704.126	+	584.423i	0.464290	+	0.385360i
$133$	−1948.36	−	1124.89i	−1.27026	−	0.733384i
$134$	−492.643	−	977.586i	−0.317596	−	0.630228i
$135$	−524.081	−	1405.42i	−0.334116	−	0.895996i
$136$	−138.956	+	807.487i	−0.0876131	+	0.509128i
$137$	−1793.30	−	1035.36i	−1.11833	−	0.645671i	−0.177359	−	0.984146i	$-0.556755\pi$
$137$	−1793.30	−	1035.36i	−1.11833	−	0.645671i	−0.940975	+	0.338476i	$0.890089\pi$
$138$	1035.30	+	2373.98i	0.638625	+	1.46439i
$139$	874.266	+	1514.27i	0.533484	+	0.924022i	0.999235	+	0.0391059i	$0.0124510\pi$
$139$	874.266	+	1514.27i	0.533484	+	0.924022i	−0.465751	+	0.884916i	$0.654216\pi$
$140$	−173.732	+	1522.61i	−0.104879	+	0.919170i
$141$	1309.75	−	2002.79i	0.782274	−	1.19621i
$142$	−57.5504	−	3.27268i	−0.0340107	−	0.00193407i
$143$	−455.146			−0.266163
$144$	1630.04	+	573.552i	0.943309	+	0.331917i
$145$	−1653.50			−0.947003
$146$	−1046.06	−	59.4858i	−0.592964	−	0.0337197i
$147$	51.4992	+	101.877i	0.0288951	+	0.0571610i
$148$	202.840	−	1777.72i	0.112658	−	0.987347i
$149$	51.5884	+	89.3538i	0.0283644	+	0.0491285i	0.879859	−	0.475235i	$-0.157637\pi$
$149$	51.5884	+	89.3538i	0.0283644	+	0.0491285i	−0.851495	+	0.524363i	$0.824303\pi$
$150$	−93.3566	+	126.451i	−0.0508169	+	0.0688310i
$151$	2205.07	+	1273.10i	1.18838	+	0.686114i	0.957939	−	0.286971i	$-0.0926483\pi$
$151$	2205.07	+	1273.10i	1.18838	+	0.686114i	0.230446	+	0.973085i	$0.425982\pi$
$152$	−2800.03	−	481.843i	−1.49416	−	0.257122i
$153$	−108.412	+	971.661i	−0.0572847	+	0.513426i
$154$	−502.037	−	996.226i	−0.262697	−	0.521287i
$155$	2605.49	+	1504.28i	1.35018	+	0.779528i
$156$	−806.071	+	298.294i	−0.413701	+	0.153094i
$157$	154.698	−	89.3150i	0.0786386	−	0.0454020i	−0.460165	−	0.887833i	$-0.652210\pi$
$157$	154.698	−	89.3150i	0.0786386	−	0.0454020i	0.538804	+	0.842431i	$0.318876\pi$
$158$	1537.11	+	1007.96i	0.773964	+	0.507524i
$159$	819.865	+	45.5962i	0.408928	+	0.0227422i
$160$	459.233	+	1880.07i	0.226910	+	0.928953i
$161$		−	3157.41i		−	1.54558i
$162$	1982.17	+	567.908i	0.961322	+	0.275426i
$163$	2230.94			1.07203			0.536014	−	0.844209i	$-0.319929\pi$
$163$	2230.94			1.07203			0.536014	+	0.844209i	$0.319929\pi$
$164$	400.784	−	174.188i	0.190829	−	0.0829377i
$165$	−67.9064	+	1221.03i	−0.0320394	+	0.576101i
$166$	1410.54	+	924.955i	0.659512	+	0.432472i
$167$	922.538	+	1597.88i	0.427474	+	0.740406i	0.996648	−	0.0818106i	$-0.0260703\pi$
$167$	922.538	+	1597.88i	0.427474	+	0.740406i	−0.569174	+	0.822217i	$0.692737\pi$
$168$	−1542.02	−	1435.31i	−0.708152	−	0.659145i
$169$	−884.747	+	1532.43i	−0.402707	+	0.697509i
$170$	−977.856	+	492.779i	−0.441165	+	0.222320i
$171$	−3369.32	−	375.927i	−1.50677	−	0.168116i
$172$	1498.54	−	2024.47i	0.664320	−	0.897469i
$173$	−1557.87	+	2698.32i	−0.684642	+	1.18583i	0.288908	+	0.957357i	$0.406708\pi$
$173$	−1557.87	+	2698.32i	−0.684642	+	1.18583i	−0.973549	+	0.228477i	$0.926625\pi$
$174$	1350.04	−	1828.62i	0.588198	−	0.796710i
$175$	165.948	−	95.8100i	0.0716827	−	0.0413860i
$176$	−1030.04	−	961.161i	−0.441149	−	0.411649i
$177$	2163.18	−	1093.50i	0.918613	−	0.464363i
$178$	194.354	−	3417.72i	0.0818394	−	1.43915i
$179$		−	2456.16i		−	1.02560i	−0.858509	−	0.512799i	$-0.828609\pi$
$179$		−	2456.16i		−	1.02560i	0.858509	−	0.512799i	$-0.171391\pi$
$180$	679.971	+	2206.96i	0.281567	+	0.913872i
$181$			3026.42i			1.24283i	0.783482	+	0.621415i	$0.213442\pi$
$181$			3026.42i			1.24283i	−0.783482	+	0.621415i	$0.786558\pi$
$182$	1046.14	+	59.4900i	0.426071	+	0.0242291i
$183$	−1919.68	−	1255.40i	−0.775446	−	0.507113i
$184$	−1379.19	−	3741.30i	−0.552584	−	1.49898i
$185$	2070.83	−	1195.60i	0.822977	−	0.475146i
$186$	−3790.93	+	1653.23i	−1.49443	+	0.651725i
$187$	398.554	−	690.316i	0.155857	−	0.269951i
$188$	−2192.00	+	2961.30i	−0.850361	+	1.14880i
$189$	−1938.27	−	1600.61i	−0.745972	−	0.616016i
$190$	−1708.76	−	3390.80i	−0.652454	−	1.29471i
$191$	−976.763	+	1691.80i	−0.370032	+	0.640914i	−0.989570	−	0.144052i	$-0.953987\pi$
$191$	−976.763	+	1691.80i	−0.370032	+	0.640914i	0.619538	+	0.784967i	$0.287320\pi$
$192$	−2454.14	−	1027.16i	−0.922462	−	0.386089i
$193$	807.292	+	1398.27i	0.301089	+	0.521501i	0.976383	−	0.216047i	$-0.0693165\pi$
$193$	807.292	+	1398.27i	0.301089	+	0.521501i	−0.675294	+	0.737549i	$0.735983\pi$
$194$	−2465.17	+	3759.33i	−0.912313	+	1.39126i
$195$	−961.331	−	628.674i	−0.353037	−	0.230873i
$196$	−70.0542	−	161.186i	−0.0255299	−	0.0587412i
$197$	3469.85			1.25491			0.627453	−	0.778654i	$-0.284097\pi$
$197$	3469.85			1.25491			0.627453	+	0.778654i	$0.284097\pi$
$198$	−1294.90	−	1072.04i	−0.464771	−	0.384780i
$199$			1323.61i			0.471500i	0.971814	+	0.235750i	$0.0757546\pi$
$199$			1323.61i			0.471500i	−0.971814	+	0.235750i	$0.924245\pi$
$200$	154.785	−	186.016i	0.0547249	−	0.0657666i
$201$	907.284	+	1794.81i	0.318383	+	0.629831i
$202$	1974.26	−	3010.71i	0.687665	−	1.04868i
$203$	−2399.80	+	1385.52i	−0.829718	+	0.479038i
$204$	253.427	−	1483.77i	0.0869776	−	0.509237i
$205$	505.773	+	292.008i	0.172316	+	0.0994865i
$206$	−3471.71	+	1749.53i	−1.17420	+	0.591726i
$207$	−1907.40	−	4358.90i	−0.640452	−	1.46360i
$208$	1265.58	−	386.474i	0.421887	−	0.128832i
$209$	2393.73	+	1382.02i	0.792239	+	0.457400i
$210$	315.675	−	2797.60i	0.103732	−	0.919300i
$211$	−73.6849	−	127.626i	−0.0240411	−	0.0416405i	0.853755	−	0.520676i	$-0.174320\pi$
$211$	−73.6849	−	127.626i	−0.0240411	−	0.0416405i	−0.877796	+	0.479035i	$0.840987\pi$
$212$	−1256.06	−	143.319i	−0.406919	−	0.0464302i
$213$	105.734	+	5.88033i	0.0340131	+	0.00189161i
$214$	−258.975	+	4554.10i	−0.0827251	+	1.45473i
$215$	3366.12			1.06775
$216$	−2995.88	−	1049.94i	−0.943722	−	0.330739i
$217$	5041.96			1.57728
$218$	248.366	−	4367.54i	0.0771628	−	1.35691i
$219$	1921.88	+	106.884i	0.593006	+	0.0329796i
$220$	213.445	−	1870.66i	0.0654113	−	0.573272i
$221$	374.351	+	648.394i	0.113944	+	0.197356i
$222$	−368.565	+	3266.34i	−0.111426	+	0.987487i
$223$	−1045.36	−	603.537i	−0.313911	−	0.181237i	0.334764	−	0.942302i	$-0.391343\pi$
$223$	−1045.36	−	603.537i	−0.313911	−	0.181237i	−0.648675	+	0.761065i	$0.724677\pi$
$224$	2241.88	+	2343.82i	0.668715	+	0.699122i
$225$	171.217	−	232.519i	0.0507309	−	0.0688944i
$226$	−3479.82	+	1753.62i	−1.02422	+	0.516146i
$227$	−461.434	−	266.409i	−0.134918	−	0.0778951i	0.431022	−	0.902342i	$-0.358153\pi$
$227$	−461.434	−	266.409i	−0.134918	−	0.0778951i	−0.565940	+	0.824447i	$0.691487\pi$
$228$	5145.09	+	878.780i	1.49448	+	0.255257i
$229$	438.805	−	253.344i	0.126625	−	0.0731069i	−0.435350	−	0.900261i	$-0.643375\pi$
$229$	438.805	−	253.344i	0.126625	−	0.0731069i	0.561974	+	0.827155i	$0.310042\pi$
$230$	2922.15	−	4456.22i	0.837742	−	1.27754i
$231$	924.584	+	1829.03i	0.263347	+	0.520958i
$232$	−2238.37	+	2690.01i	−0.633433	+	0.761240i
$233$			401.945i			0.113014i	0.998402	+	0.0565070i	$0.0179963\pi$
$233$			401.945i			0.113014i	−0.998402	+	0.0565070i	$0.982004\pi$
$234$	1480.16	−	549.848i	0.413510	−	0.153610i
$235$	−4923.79			−1.36678
$236$	−3422.50	+	1487.48i	−0.944008	+	0.410282i
$237$	−2826.17	−	1848.21i	−0.774596	−	0.506557i
$238$	−1006.29	+	1534.57i	−0.274068	+	0.417948i
$239$	−437.215	−	757.279i	−0.118331	−	0.204955i	0.800775	−	0.598965i	$-0.204421\pi$
$239$	−437.215	−	757.279i	−0.118331	−	0.204955i	−0.919106	+	0.394010i	$0.871088\pi$
$240$	−847.976	−	3452.85i	−0.228069	−	0.928670i
$241$	−479.685	+	830.839i	−0.128213	+	0.222071i	−0.922984	−	0.384838i	$-0.874257\pi$
$241$	−479.685	+	830.839i	−0.128213	+	0.222071i	0.794772	+	0.606909i	$0.207591\pi$
$242$	−1077.38	−	2137.93i	−0.286186	−	0.567898i
$243$	−3642.78	−	1038.77i	−0.961665	−	0.274226i
$244$	2838.41	+	2101.04i	0.744717	+	0.551250i
$245$	117.439	−	203.410i	0.0306240	−	0.0530424i
$246$	−735.887	+	320.922i	−0.190725	+	0.0831758i
$247$	−2248.37	+	1298.09i	−0.579191	+	0.334396i
$248$	5974.36	−	2202.39i	1.52973	−	0.563919i
$249$	−2593.44	−	1696.01i	−0.660051	−	0.431649i
$250$	4096.75	+	232.967i	1.03641	+	0.0589366i
$251$		−	1486.12i		−	0.373719i	−0.982387	−	0.186859i	$-0.940169\pi$
$251$		−	1486.12i		−	0.373719i	0.982387	−	0.186859i	$-0.0598308\pi$
$252$	2836.16	+	2633.29i	0.708974	+	0.658260i
$253$			3879.15i			0.963953i
$254$	42.7270	−	751.359i	0.0105549	−	0.185608i
$255$	1795.30	−	907.535i	0.440888	−	0.222871i
$256$	3680.28	+	1797.98i	0.898506	+	0.438960i
$257$	810.352	−	467.857i	0.196686	−	0.113557i	−0.398423	−	0.917202i	$-0.630442\pi$
$257$	810.352	−	467.857i	0.196686	−	0.113557i	0.595109	+	0.803645i	$0.297109\pi$
$258$	−2748.36	+	3722.63i	−0.663199	+	0.898297i
$259$	2003.66	−	3470.45i	0.480701	−	0.832599i
$260$	1421.41	+	1052.15i	0.339047	+	0.250968i
$261$	−2475.99	+	3362.49i	−0.587203	+	0.797443i
$262$	828.415	−	417.470i	0.195342	−	0.0984405i
$263$	723.768	−	1253.60i	0.169694	−	0.293918i	−0.768619	−	0.639707i	$-0.779056\pi$
$263$	723.768	−	1253.60i	0.169694	−	0.293918i	0.938312	+	0.345789i	$0.112389\pi$
$264$	1894.51	+	1763.40i	0.441663	+	0.411098i
$265$	−844.762	−	1463.17i	−0.195824	−	0.339177i
$266$	−5321.27	−	3489.40i	−1.22657	−	0.804319i
$267$	−349.213	+	6279.20i	−0.0800431	+	1.43925i
$268$	−1234.17	−	2839.68i	−0.281303	−	0.647243i
$269$	2458.16			0.557161			0.278581	−	0.960413i	$-0.410136\pi$
$269$	2458.16			0.557161			0.278581	+	0.960413i	$0.410136\pi$
$270$	−1254.25	−	4052.88i	−0.282708	−	0.913520i
$271$		−	484.315i		−	0.108561i	−0.998526	−	0.0542806i	$-0.982713\pi$
$271$		−	484.315i		−	0.108561i	0.998526	−	0.0542806i	$-0.0172865\pi$
$272$	−522.062	+	2257.92i	−0.116377	+	0.503333i
$273$	−1922.01	−	106.891i	−0.426100	−	0.0236973i
$274$	−4897.77	−	3211.69i	−1.07987	−	0.708122i
$275$	−203.882	+	117.711i	−0.0447074	+	0.0258118i
$276$	2542.32	+	6870.04i	0.554455	+	1.49829i
$277$	−3576.88	−	2065.11i	−0.775862	−	0.447944i	0.0590999	−	0.998252i	$-0.481177\pi$
$277$	−3576.88	−	2065.11i	−0.775862	−	0.447944i	−0.834962	+	0.550308i	$0.814510\pi$
$278$	2225.64	+	4416.50i	0.480163	+	0.952820i
$279$	6960.58	−	3045.87i	1.49362	−	0.653589i
$280$	−735.101	+	4271.74i	−0.156895	+	0.911733i
$281$	734.232	+	423.909i	0.155874	+	0.0899939i	0.575908	−	0.817514i	$-0.304649\pi$
$281$	734.232	+	423.909i	0.155874	+	0.0899939i	−0.420034	+	0.907508i	$0.637982\pi$
$282$	4020.17	−	5445.28i	0.848927	−	1.14986i
$283$	2706.55	+	4687.88i	0.568507	+	0.984683i	0.996714	+	0.0810026i	$0.0258122\pi$
$283$	2706.55	+	4687.88i	0.568507	+	0.984683i	−0.428207	+	0.903681i	$0.640854\pi$
$284$	−161.989	−	18.4832i	−0.0338461	−	0.00386189i
$285$	3146.96	+	6225.38i	0.654069	+	1.29389i
$286$	−1285.27	−	73.0887i	−0.265733	−	0.0151113i
$287$	978.735			0.201299
$288$	4510.90	+	1881.39i	0.922943	+	0.384937i
$289$	3601.78			0.733113
$290$	−4669.25	−	265.523i	−0.945476	−	0.0537658i
$291$	4520.18	−	6911.98i	0.910575	−	1.39240i
$292$	−2944.39	−	335.960i	−0.590094	−	0.0673307i
$293$	−4158.79	−	7203.24i	−0.829213	−	1.43624i	−0.898657	−	0.438653i	$-0.855456\pi$
$293$	−4158.79	−	7203.24i	−0.829213	−	1.43624i	0.0694441	−	0.997586i	$-0.477877\pi$
$294$	129.067	+	295.956i	0.0256032	+	0.0587093i
$295$	−4319.06	−	2493.61i	−0.852424	−	0.492147i
$296$	858.265	−	4987.46i	0.168533	−	0.979359i
$297$	2381.34	+	1966.49i	0.465251	+	0.384199i
$298$	131.330	+	260.607i	0.0255294	+	0.0506596i
$299$	−3155.43	−	1821.79i	−0.610312	−	0.352364i
$300$	−283.932	+	342.088i	−0.0546428	+	0.0658349i
$301$	4885.40	−	2820.59i	0.935514	−	0.540119i
$302$	6022.38	+	3949.15i	1.14751	+	0.752478i
$303$	−3620.04	+	5535.54i	−0.686356	+	1.04953i
$304$	−7829.54	−	1810.30i	−1.47715	−	0.341538i
$305$			4719.47i			0.886020i
$306$	−462.172	+	2726.43i	−0.0863419	+	0.509345i
$307$	−7799.02			−1.44988			−0.724940	−	0.688812i	$-0.758133\pi$
$307$	−7799.02			−1.44988			−0.724940	+	0.688812i	$0.758133\pi$
$308$	−1257.71	−	2893.83i	−0.232677	−	0.535360i
$309$	6373.92	−	3222.05i	1.17346	−	0.593191i
$310$	7115.99	+	4666.28i	1.30375	+	0.854926i
$311$	−2762.34	−	4784.52i	−0.503660	−	0.872364i	−0.999991	−	0.00423108i	$-0.998653\pi$
$311$	−2762.34	−	4784.52i	−0.503660	−	0.872364i	0.496331	−	0.868133i	$-0.334680\pi$
$312$	−2324.14	+	712.900i	−0.421726	+	0.129359i
$313$	−1521.85	+	2635.91i	−0.274824	+	0.476008i	−0.970091	−	0.242743i	$-0.921953\pi$
$313$	−1521.85	+	2635.91i	−0.274824	+	0.476008i	0.695267	+	0.718752i	$0.255286\pi$
$314$	451.189	−	227.372i	0.0810894	−	0.0408641i
$315$	−573.516	+	5140.25i	−0.102584	+	0.919429i
$316$	4178.74	+	3093.17i	0.743901	+	0.550646i
$317$	−3235.14	+	5603.42i	−0.573197	+	0.992806i	0.423038	+	0.906112i	$0.360964\pi$
$317$	−3235.14	+	5603.42i	−0.573197	+	0.992806i	−0.996235	+	0.0866940i	$0.972370\pi$
$318$	2307.87	+	260.414i	0.406977	+	0.0459222i
$319$	2948.36	−	1702.24i	0.517482	−	0.298768i
$320$	994.906	+	5382.81i	0.173803	+	0.940338i
$321$	465.325	−	8367.01i	0.0809094	−	1.45483i
$322$	507.025	−	8916.09i	0.0877497	−	1.54309i
$323$		−	4546.77i		−	0.783247i
$324$	5506.19	+	1922.00i	0.944134	+	0.329561i
$325$		−	221.125i		−	0.0377410i
$326$	6299.87	+	358.251i	1.07030	+	0.0608640i
$327$	−446.263	+	8024.26i	−0.0754691	+	1.35701i
$328$	1159.73	−	427.524i	0.195230	−	0.0719696i
$329$	−7146.13	+	4125.82i	−1.19750	+	0.691379i
$330$	−387.834	+	3437.11i	−0.0646957	+	0.573353i
$331$	−3283.78	+	5687.67i	−0.545295	+	0.944479i	0.453293	+	0.891361i	$0.350249\pi$
$331$	−3283.78	+	5687.67i	−0.545295	+	0.944479i	−0.998588	+	0.0531172i	$0.983084\pi$
$332$	3834.64	+	2838.46i	0.633895	+	0.469218i
$333$	669.607	−	6001.48i	0.110193	−	0.987625i
$334$	2348.53	+	4660.35i	0.384748	+	0.763482i
$335$	2068.97	−	3583.56i	0.337432	−	0.584450i
$336$	−4123.97	−	4300.74i	−0.669587	−	0.698287i
$337$	−5965.59	−	10332.7i	−0.964292	−	1.67020i	−0.711506	−	0.702680i	$-0.751986\pi$
$337$	−5965.59	−	10332.7i	−0.964292	−	1.67020i	−0.252786	−	0.967522i	$-0.581347\pi$
$338$	−2744.49	+	4185.29i	−0.441658	+	0.673520i
$339$	6388.82	−	3229.58i	1.02358	−	0.517424i
$340$	−2840.46	+	1234.52i	−0.453076	+	0.196915i
$341$	−6194.49			−0.983726
$342$	−9454.14	−	1602.62i	−1.49480	−	0.253392i
$343$		−	6539.27i		−	1.02941i
$344$	4556.78	−	5476.20i	0.714201	−	0.858305i
$345$	−5358.11	+	8193.29i	−0.836147	+	1.27859i
$346$	−4832.53	+	7369.52i	−0.750863	+	1.14505i
$347$	−1257.88	+	726.237i	−0.194601	+	0.112353i	−0.594135	−	0.804366i	$-0.702505\pi$
$347$	−1257.88	+	726.237i	−0.194601	+	0.112353i	0.399534	+	0.916718i	$0.369172\pi$
$348$	4105.99	−	4946.99i	0.632482	−	0.762030i
$349$	−2775.33	−	1602.34i	−0.425673	−	0.245763i	0.271828	−	0.962346i	$-0.412372\pi$
$349$	−2775.33	−	1602.34i	−0.425673	−	0.245763i	−0.697502	+	0.716583i	$0.745705\pi$
$350$	484.000	−	243.906i	0.0739168	−	0.0372495i
$351$	−2717.97	+	1013.53i	−0.413318	+	0.154126i
$352$	−2754.35	−	2879.59i	−0.417067	−	0.436031i
$353$	3481.39	+	2009.98i	0.524917	+	0.303061i	0.738944	−	0.673767i	$-0.235325\pi$
$353$	3481.39	+	2009.98i	0.524917	+	0.303061i	−0.214027	+	0.976828i	$0.568658\pi$
$354$	6284.12	−	2740.52i	0.943495	−	0.411460i
$355$	−108.945	−	188.698i	−0.0162879	−	0.0282115i
$356$	1097.66	−	9619.98i	0.163415	−	1.43219i
$357$	1845.15	−	2821.50i	0.273546	−	0.418290i
$358$	394.417	−	6935.86i	0.0582279	−	1.02394i
$359$	−4423.07			−0.650253			−0.325126	−	0.945671i	$-0.605407\pi$
$359$	−4423.07			−0.650253			−0.325126	+	0.945671i	$0.605407\pi$
$360$	1565.75	+	6341.35i	0.229228	+	0.928384i
$361$	8907.32			1.29863
$362$	−485.992	+	8546.21i	−0.0705612	+	1.24082i
$363$	1984.18	+	3925.15i	0.286894	+	0.567540i
$364$	2944.60	+	335.983i	0.424008	+	0.0483800i
$365$	−1980.24	−	3429.87i	−0.283974	−	0.491857i
$366$	−5219.31	−	3853.34i	−0.745404	−	0.550320i
$367$	−1037.58	−	599.048i	−0.147579	−	0.0852045i	0.424392	−	0.905478i	$-0.360488\pi$
$367$	−1037.58	−	599.048i	−0.147579	−	0.0852045i	−0.571971	+	0.820274i	$0.693821\pi$
$368$	−3293.87	−	10786.4i	−0.466589	−	1.52793i
$369$	1351.17	−	591.258i	0.190622	−	0.0834138i
$370$	6039.75	−	3043.66i	0.848626	−	0.427655i
$371$	−2452.08	−	1415.71i	−0.343142	−	0.198113i
$372$	−10970.5	+	4059.74i	−1.52902	+	0.565828i
$373$	−1831.97	+	1057.69i	−0.254305	+	0.146823i	−0.621734	−	0.783229i	$-0.713571\pi$
$373$	−1831.97	+	1057.69i	−0.254305	+	0.146823i	0.367429	+	0.930052i	$0.380238\pi$
$374$	1236.32	−	1885.36i	0.170932	−	0.260667i
$375$	−7526.75	−	418.594i	−1.03648	−	0.0576430i
$376$	−6665.44	+	8010.32i	−0.914213	+	1.09867i
$377$			3197.73i			0.436847i
$378$	−5216.40	−	4831.15i	−0.709795	−	0.657375i
$379$	−4201.28			−0.569406			−0.284703	−	0.958616i	$-0.591895\pi$
$379$	−4201.28			−0.569406			−0.284703	+	0.958616i	$0.591895\pi$
$380$	−4280.79	−	9849.57i	−0.577895	−	1.32966i
$381$	−76.7716	+	1380.43i	−0.0103232	+	0.185621i
$382$	−3029.92	+	4620.57i	−0.405823	+	0.618872i
$383$	1040.16	+	1801.61i	0.138772	+	0.240360i	0.927032	−	0.374982i	$-0.122351\pi$
$383$	1040.16	+	1801.61i	0.138772	+	0.240360i	−0.788260	+	0.615342i	$0.789018\pi$
$384$	−6765.23	−	3294.66i	−0.899054	−	0.437839i
$385$	2108.42	−	3651.89i	0.279104	−	0.483422i
$386$	2055.15	+	4078.17i	0.270995	+	0.537754i
$387$	5040.52	−	6845.20i	0.662077	−	0.899124i
$388$	−7564.98	+	10220.0i	−0.989829	+	1.33722i
$389$	1695.86	−	2937.32i	0.221038	−	0.382848i	−0.734086	−	0.679057i	$-0.762389\pi$
$389$	1695.86	−	2937.32i	0.221038	−	0.382848i	0.955123	+	0.296208i	$0.0957223\pi$
$390$	−2613.71	−	1929.66i	−0.339360	−	0.250544i
$391$	5526.18	−	3190.54i	0.714759	−	0.412666i
$392$	−171.940	−	466.416i	−0.0221538	−	0.0600959i
$393$	−1520.94	+	768.841i	−0.195219	+	0.0986842i
$394$	9798.38	+	557.198i	1.25288	+	0.0712468i
$395$			6948.05i			0.885049i
$396$	−3484.48	−	3235.23i	−0.442176	−	0.410546i
$397$			2852.23i			0.360577i	0.983614	+	0.180289i	$0.0577031\pi$
$397$			2852.23i			0.360577i	−0.983614	+	0.180289i	$0.942297\pi$
$398$	−212.550	+	3737.70i	−0.0267692	+	0.470739i
$399$	9783.79	+	6398.23i	1.22757	+	0.802788i
$400$	466.964	−	500.428i	0.0583705	−	0.0625536i
$401$	784.032	−	452.661i	0.0976376	−	0.0563711i	−0.450386	−	0.892834i	$-0.648714\pi$
$401$	784.032	−	452.661i	0.0976376	−	0.0563711i	0.548024	+	0.836463i	$0.315380\pi$
$402$	2273.83	+	5213.99i	0.282111	+	0.646891i
$403$	2909.15	−	5038.80i	0.359591	−	0.622831i
$404$	6058.51	−	8184.80i	0.746094	−	1.00794i
$405$	2313.49	+	7442.73i	0.283848	+	0.913167i
$406$	−6999.19	+	3527.16i	−0.855577	+	0.431158i
$407$	−2461.68	+	4263.75i	−0.299806	+	0.519279i
$408$	953.910	−	4149.26i	0.115749	−	0.503477i
$409$	−3943.23	−	6829.88i	−0.476724	−	0.825711i	0.522920	−	0.852382i	$-0.324843\pi$
$409$	−3943.23	−	6829.88i	−0.476724	−	0.825711i	−0.999644	+	0.0266709i	$0.991509\pi$
$410$	1381.34	+	905.810i	0.166389	+	0.109109i
$411$	9005.14	+	5889.02i	1.08076	+	0.706774i
$412$	−10084.6	+	4382.94i	−1.20590	+	0.524106i
$413$	−8357.93			−0.995803
$414$	−4686.28	−	12615.2i	−0.556324	−	1.49760i
$415$			6375.90i			0.754170i
$416$	3635.90	−	888.119i	0.428521	−	0.104672i
$417$	−4098.89	−	8108.51i	−0.481352	−	0.952220i
$418$	6537.65	+	4287.04i	0.764993	+	0.501641i
$419$	12290.9	−	7096.16i	1.43306	−	0.827375i	0.435703	−	0.900091i	$-0.356500\pi$
$419$	12290.9	−	7096.16i	1.43306	−	0.827375i	0.997353	+	0.0727158i	$0.0231666\pi$
$420$	1340.67	−	7849.37i	0.155757	−	0.911928i
$421$	13997.7	+	8081.57i	1.62044	+	0.935562i	0.986802	+	0.161935i	$0.0517733\pi$
$421$	13997.7	+	8081.57i	1.62044	+	0.935562i	0.633640	+	0.773628i	$0.281560\pi$
$422$	−187.582	−	372.231i	−0.0216382	−	0.0429382i
$423$	−7373.02	+	10012.8i	−0.847491	+	1.15092i
$424$	−3523.94	−	606.416i	−0.403627	−	0.0694580i
$425$	335.379	+	193.631i	0.0382782	+	0.0221000i
$426$	297.635	+	33.5844i	0.0338509	+	0.00381965i
$427$	3954.61	+	6849.58i	0.448189	+	0.776287i
$428$	−1462.62	+	12818.6i	−0.165183	+	1.44769i
$429$	2361.36	+	131.325i	0.265752	+	0.0147796i
$430$	9505.46	+	540.541i	1.06603	+	0.0606214i
$431$	9955.69			1.11264			0.556321	−	0.830968i	$-0.312213\pi$
$431$	9955.69			1.11264			0.556321	+	0.830968i	$0.312213\pi$
$432$	−8291.37	−	3445.99i	−0.923422	−	0.383785i
$433$	−3785.69			−0.420158			−0.210079	−	0.977684i	$-0.567372\pi$
$433$	−3785.69			−0.420158			−0.210079	+	0.977684i	$0.567372\pi$
$434$	14237.8	+	809.652i	1.57474	+	0.0895497i
$435$	8578.57	+	477.091i	0.945542	+	0.0525856i
$436$	1402.71	−	12293.5i	0.154077	−	1.35035i
$437$	11063.5	+	19162.5i	1.21107	+	2.09764i
$438$	5409.95	+	610.446i	0.590177	+	0.0665941i
$439$	13629.0	+	7868.72i	1.48173	+	0.855475i	0.999785	−	0.0207289i	$-0.00659870\pi$
$439$	13629.0	+	7868.72i	1.48173	+	0.855475i	0.481941	+	0.876204i	$0.339932\pi$
$440$	903.136	−	5248.21i	0.0978530	−	0.568633i
$441$	−237.790	−	543.410i	−0.0256765	−	0.0586773i
$442$	952.994	+	1891.09i	0.102555	+	0.203507i
$443$	5151.93	+	2974.47i	0.552541	+	0.319010i	0.750146	−	0.661272i	$-0.229983\pi$
$443$	5151.93	+	2974.47i	0.552541	+	0.319010i	−0.197605	+	0.980282i	$0.563316\pi$
$444$	−1565.30	+	9164.51i	−0.167310	+	0.979568i
$445$	11206.2	−	6469.88i	1.19376	−	0.689218i
$446$	−2855.03	−	1872.17i	−0.303115	−	0.198767i
$447$	−241.866	−	478.465i	−0.0255926	−	0.0506277i
$448$	5954.40	+	6978.65i	0.627944	+	0.735960i
$449$			15116.6i			1.58886i	0.607356	+	0.794430i	$0.292230\pi$
$449$			15116.6i			1.58886i	−0.607356	+	0.794430i	$0.707770\pi$
$450$	520.832	−	629.106i	0.0545605	−	0.0659030i
$451$	−1202.46			−0.125547
$452$	−10108.2	+	4393.18i	−1.05188	+	0.457163i
$453$	−11072.9	−	7241.24i	−1.14845	−	0.751045i
$454$	−1260.25	−	826.401i	−0.130278	−	0.0854294i
$455$	1980.38	+	3430.11i	0.204047	+	0.353420i
$456$	14387.9	+	3307.77i	1.47758	+	0.339694i
$457$	1777.87	−	3079.37i	0.181981	−	0.315201i	−0.760574	−	0.649251i	$-0.775082\pi$
$457$	1777.87	−	3079.37i	0.181981	−	0.315201i	0.942555	+	0.334051i	$0.108416\pi$
$458$	1279.81	−	644.946i	0.130571	−	0.0657999i
$459$	842.812	−	5009.83i	0.0857061	−	0.509452i
$460$	8967.34	−	12114.5i	0.908923	−	1.22792i
$461$	4424.78	−	7663.95i	0.447034	−	0.774286i	−0.551157	−	0.834401i	$-0.685814\pi$
$461$	4424.78	−	7663.95i	0.447034	−	0.774286i	0.998191	+	0.0601155i	$0.0191469\pi$
$462$	2317.19	+	5313.41i	0.233345	+	0.535070i
$463$	−11428.3	+	6598.13i	−1.14712	+	0.662292i	−0.948185	−	0.317720i	$-0.897083\pi$
$463$	−11428.3	+	6598.13i	−1.14712	+	0.662292i	−0.198939	+	0.980012i	$0.563750\pi$
$464$	−6752.84	+	7236.77i	−0.675631	+	0.724049i
$465$	−13083.6	−	8556.19i	−1.30481	−	0.853298i
$466$	−64.5455	+	1135.04i	−0.00641633	+	0.112832i
$467$		−	8917.23i		−	0.883598i	−0.897114	−	0.441799i	$-0.854340\pi$
$467$		−	8917.23i		−	0.883598i	0.897114	−	0.441799i	$-0.145660\pi$
$468$	4268.08	−	1315.01i	0.421564	−	0.129885i
$469$		−	6934.64i		−	0.682755i
$470$	−13904.1	−	790.677i	−1.36457	−	0.0775983i
$471$	−828.365	+	418.743i	−0.0810383	+	0.0409653i
$472$	−9903.55	+	3650.84i	−0.965779	+	0.356025i
$473$	−6002.15	+	3465.34i	−0.583465	+	0.336864i
$474$	−7683.93	−	5672.93i	−0.744587	−	0.549717i
$475$	−671.433	+	1162.96i	−0.0648578	+	0.112337i
$476$	−3088.05	+	4171.83i	−0.297354	+	0.401714i
$477$	−4240.41	−	473.118i	−0.407034	−	0.0454142i
$478$	−1113.03	−	2208.66i	−0.106504	−	0.211343i
$479$	−3252.43	+	5633.38i	−0.310245	+	0.537360i	−0.978415	−	0.206648i	$-0.933744\pi$
$479$	−3252.43	+	5633.38i	−0.310245	+	0.537360i	0.668170	+	0.744009i	$0.267078\pi$
$480$	−1840.10	−	9886.56i	−0.174977	−	0.940120i
$481$	−2312.18	−	4004.82i	−0.219182	−	0.379634i
$482$	−1487.99	+	2269.15i	−0.140614	+	0.214433i
$483$	−911.020	+	16381.0i	−0.0858237	+	1.54320i
$484$	−2699.07	−	6210.23i	−0.253482	−	0.583230i
$485$	−16992.9			−1.59094
$486$	−10119.9	−	3518.31i	−0.944545	−	0.328382i
$487$		−	20850.6i		−	1.94010i	−0.242898	−	0.970052i	$-0.578098\pi$
$487$		−	20850.6i		−	1.94010i	0.242898	−	0.970052i	$-0.421902\pi$
$488$	7677.91	+	6388.84i	0.712219	+	0.592642i
$489$	−11574.4	−	643.703i	−1.07037	−	0.0595281i
$490$	364.295	−	555.543i	0.0335861	−	0.0512181i
$491$	−3316.39	+	1914.72i	−0.304820	+	0.175988i	−0.644606	−	0.764515i	$-0.722979\pi$
$491$	−3316.39	+	1914.72i	−0.304820	+	0.175988i	0.339786	+	0.940503i	$0.389645\pi$
$492$	−2129.58	+	788.070i	−0.195140	+	0.0722133i
$493$	−4849.96	−	2800.13i	−0.443065	−	0.255804i
$494$	−6557.53	+	3304.59i	−0.597242	+	0.300973i
$495$	704.615	−	6315.25i	0.0639800	−	0.573433i
$496$	17224.5	−	5259.87i	1.55928	−	0.476160i
$497$	−316.234	−	182.578i	−0.0285413	−	0.0164783i
$498$	−7051.18	−	5205.78i	−0.634480	−	0.468427i
$499$	1634.90	+	2831.73i	0.146670	+	0.254040i	0.929995	−	0.367573i	$-0.119811\pi$
$499$	1634.90	+	2831.73i	0.146670	+	0.254040i	−0.783325	+	0.621613i	$0.786478\pi$
$500$	11531.3	+	1315.74i	1.03139	+	0.117683i
$501$	−4325.21	−	8556.22i	−0.385701	−	0.763001i
$502$	238.646	−	4196.62i	0.0212177	−	0.373116i
$503$	−15404.4			−1.36550			−0.682750	−	0.730652i	$-0.739216\pi$
$503$	−15404.4			−1.36550			−0.682750	+	0.730652i	$0.739216\pi$
$504$	7586.08	+	7891.49i	0.670458	+	0.697450i
$505$	13609.0			1.19919
$506$	−622.926	+	10954.2i	−0.0547281	+	0.962399i
$507$	5032.34	−	7695.16i	0.440817	−	0.674071i
$508$	241.311	−	2114.87i	0.0210757	−	0.184709i
$509$	−4493.67	−	7783.27i	−0.391314	−	0.677775i	0.601309	−	0.799016i	$-0.294646\pi$
$509$	−4493.67	−	7783.27i	−0.391314	−	0.677775i	−0.992623	+	0.121241i	$0.961313\pi$
$510$	5215.43	−	2274.46i	0.452830	−	0.197480i
$511$	−5748.02	−	3318.62i	−0.497607	−	0.287294i
$512$	10103.9	+	5668.25i	0.872135	+	0.489265i
$513$	17372.0	+	2922.53i	1.49511	+	0.251526i
$514$	2363.46	−	1191.04i	0.202816	−	0.102207i
$515$	−12726.3	−	7347.55i	−1.08891	−	0.628683i
$516$	−8358.78	+	10070.9i	−0.713130	+	0.859195i
$517$	8779.65	−	5068.93i	0.746864	−	0.431202i
$518$	6215.37	−	9478.32i	0.527196	−	0.803964i
$519$	8861.02	−	13549.7i	0.749433	−	1.14599i
$520$	3844.92	+	3199.39i	0.324252	+	0.269812i
$521$		−	14007.5i		−	1.17789i	−0.808175	−	0.588943i	$-0.799544\pi$
$521$		−	14007.5i		−	1.17789i	0.808175	−	0.588943i	$-0.200456\pi$
$522$	−7531.83	+	9097.60i	−0.631531	+	0.762819i
$523$	−12759.6			−1.06681			−0.533403	−	0.845862i	$-0.679087\pi$
$523$	−12759.6			−1.06681			−0.533403	+	0.845862i	$0.679087\pi$
$524$	2406.37	−	1045.85i	0.200616	−	0.0871912i
$525$	−888.604	+	449.194i	−0.0738702	+	0.0373418i
$526$	2245.13	−	3423.78i	0.186107	−	0.283810i
$527$	5094.87	+	8824.57i	0.421131	+	0.729420i
$528$	5066.67	+	5283.83i	0.417610	+	0.435510i
$529$	−9443.36	+	16356.4i	−0.776145	+	1.34432i
$530$	−2150.53	−	4267.45i	−0.176251	−	0.349747i
$531$	−11538.4	+	5049.06i	−0.942981	+	0.412638i
$532$	−14466.2	−	10708.1i	−1.17893	−	0.872660i
$533$	564.720	−	978.123i	0.0458925	−	0.0794882i
$534$	−1994.46	+	17675.5i	−0.161627	+	1.43239i
$535$	−14932.2	+	8621.09i	−1.20668	+	0.696677i
$536$	−3029.14	−	8217.06i	−0.244102	−	0.662170i
$537$	−708.686	+	12742.9i	−0.0569499	+	1.02402i
$538$	6941.50	+	394.738i	0.556263	+	0.0316326i
$539$			483.602i			0.0386460i
$540$	−2891.00	−	11646.2i	−0.230387	−	0.928097i
$541$			11304.7i			0.898389i	0.893434	+	0.449194i	$0.148289\pi$
$541$			11304.7i			0.898389i	−0.893434	+	0.449194i	$0.851711\pi$
$542$	77.7728	−	1367.64i	0.00616352	−	0.108386i
$543$	873.227	−	15701.5i	0.0690124	−	1.24091i
$544$	−1836.81	+	6292.22i	−0.144766	+	0.495913i
$545$	14320.5	−	8267.93i	1.12554	−	0.649833i
$546$	−5410.34	−	610.489i	−0.424068	−	0.0478507i
$547$	4074.44	−	7057.14i	0.318484	−	0.551630i	−0.661688	−	0.749779i	$-0.730160\pi$
$547$	4074.44	−	7057.14i	0.318484	−	0.551630i	0.980172	+	0.198149i	$0.0634930\pi$
$548$	−13314.9	−	9855.89i	−1.03793	−	0.768289i
$549$	9597.32	+	7067.06i	0.746091	+	0.549390i
$550$	−594.637	+	299.660i	−0.0461007	+	0.0232319i
$551$	9709.69	−	16817.7i	0.750720	−	1.30029i
$552$	6075.95	+	19808.3i	0.468496	+	1.52735i
$553$	5822.01	+	10084.0i	0.447698	+	0.775436i
$554$	−9769.00	−	6405.98i	−0.749178	−	0.491271i
$555$	−11088.7	+	5605.41i	−0.848091	+	0.428714i
$556$	5575.70	+	12829.0i	0.425292	+	0.978544i
$557$	9696.33			0.737607			0.368803	−	0.929507i	$-0.379768\pi$
$557$	9696.33			0.737607			0.368803	+	0.929507i	$0.379768\pi$
$558$	20144.9	−	7483.38i	1.52831	−	0.567736i
$559$		−	6509.79i		−	0.492549i
$560$	−2761.79	+	11944.8i	−0.208405	+	0.901355i
$561$	−2266.93	+	3466.46i	−0.170606	+	0.260880i
$562$	2005.30	+	1314.97i	0.150513	+	0.0986985i
$563$	−4632.29	+	2674.46i	−0.346763	+	0.200204i	−0.663259	−	0.748390i	$-0.730827\pi$
$563$	−4632.29	+	2674.46i	−0.346763	+	0.200204i	0.316495	+	0.948594i	$0.397494\pi$
$564$	12226.8	−	14731.2i	0.912841	−	1.09981i
$565$	−12756.1	−	7364.72i	−0.949827	−	0.548383i
$566$	6890.13	+	13672.6i	0.511685	+	1.01537i
$567$	9594.20	+	8863.43i	0.710615	+	0.656489i
$568$	−454.467	−	78.2068i	−0.0335722	−	0.00577726i
$569$	−6251.55	−	3609.33i	−0.460595	−	0.265924i	0.251700	−	0.967805i	$-0.419011\pi$
$569$	−6251.55	−	3609.33i	−0.460595	−	0.265924i	−0.712294	+	0.701881i	$0.752344\pi$
$570$	7886.90	+	18085.0i	0.579554	+	1.32894i
$571$	1605.63	+	2781.03i	0.117677	+	0.203822i	0.918847	−	0.394615i	$-0.129122\pi$
$571$	1605.63	+	2781.03i	0.117677	+	0.203822i	−0.801170	+	0.598437i	$0.795789\pi$
$572$	−3617.70	−	412.785i	−0.264447	−	0.0301738i
$573$	5555.72	−	8495.48i	0.405050	−	0.619378i
$574$	2763.82	+	157.168i	0.200975	+	0.0114287i
$575$	−1884.62			−0.136685
$576$	12436.1	+	6037.16i	0.899599	+	0.436716i
$577$	−4892.69			−0.353008			−0.176504	−	0.984300i	$-0.556479\pi$
$577$	−4892.69			−0.353008			−0.176504	+	0.984300i	$0.556479\pi$
$578$	10170.9	+	578.385i	0.731930	+	0.0416222i
$579$	−3784.89	−	7487.35i	−0.271666	−	0.537416i
$580$	−13142.7	−	1499.60i	−0.940898	−	0.107358i
$581$	5342.59	+	9253.64i	0.381494	+	0.660767i
$582$	13874.3	−	18792.6i	0.988159	−	1.33845i
$583$	3012.60	+	1739.33i	0.214012	+	0.123560i
$584$	−8260.61	−	1421.52i	−0.585319	−	0.100724i
$585$	4806.12	+	3539.02i	0.339673	+	0.250121i
$586$	−10587.2	−	21008.8i	−0.746333	−	1.48100i
$587$	−8416.04	−	4859.01i	−0.591767	−	0.341657i	0.174029	−	0.984741i	$-0.444321\pi$
$587$	−8416.04	−	4859.01i	−0.591767	−	0.341657i	−0.765796	+	0.643084i	$0.777655\pi$
$588$	316.943	+	856.467i	0.0222287	+	0.0600682i
$589$	−30600.0	+	17666.9i	−2.14066	+	1.23591i
$590$	−11796.0	−	7735.18i	−0.823108	−	0.539750i
$591$	−18002.0	−	1001.17i	−1.25297	−	0.0696830i
$592$	3224.53	−	13946.1i	0.223863	−	0.968211i
$593$			8952.48i			0.619957i	0.950744	+	0.309978i	$0.100322\pi$
$593$			8952.48i			0.619957i	−0.950744	+	0.309978i	$0.899678\pi$
$594$	6408.80	+	5935.50i	0.442688	+	0.409994i
$595$	−6936.56			−0.477935
$596$	329.009	+	757.009i	0.0226120	+	0.0520274i
$597$	381.908	−	6867.08i	0.0261816	−	0.470772i
$598$	−8617.96	−	5651.19i	−0.589322	−	0.386446i
$599$	1335.01	+	2312.30i	0.0910634	+	0.157726i	0.907959	−	0.419059i	$-0.137640\pi$
$599$	1335.01	+	2312.30i	0.0910634	+	0.157726i	−0.816895	+	0.576786i	$0.804307\pi$
$600$	−856.719	+	920.416i	−0.0582924	+	0.0626264i
$601$	10279.6	−	17804.8i	0.697692	−	1.20844i	−0.271572	−	0.962418i	$-0.587544\pi$
$601$	10279.6	−	17804.8i	0.697692	−	1.20844i	0.969265	−	0.246021i	$-0.0791231\pi$
$602$	14248.6	−	7180.44i	0.964670	−	0.486135i
$603$	−4189.25	−	9573.49i	−0.282918	−	0.646539i
$604$	16372.2	+	12119.0i	1.10294	+	0.816414i
$605$	4524.73	−	7837.06i	0.304060	−	0.526647i
$606$	−11111.4	+	15050.3i	−0.744836	+	1.00887i
$607$	10811.7	−	6242.12i	0.722952	−	0.417396i	−0.0928863	−	0.995677i	$-0.529609\pi$
$607$	10811.7	−	6242.12i	0.722952	−	0.417396i	0.815838	+	0.578280i	$0.196276\pi$
$608$	−21818.9	−	6369.32i	−1.45538	−	0.424852i
$609$	12850.2	−	6495.86i	0.855038	−	0.432226i
$610$	−757.866	+	13327.1i	−0.0503034	+	0.884590i
$611$			9522.21i			0.630487i
$612$	−1742.93	+	7624.85i	−0.115121	+	0.503622i
$613$			18300.4i			1.20579i	0.797822	+	0.602893i	$0.205985\pi$
$613$			18300.4i			1.20579i	−0.797822	+	0.602893i	$0.794015\pi$
$614$	−22023.4	−	1252.39i	−1.44754	−	0.0823164i
$615$	−2539.76	−	1660.91i	−0.166526	−	0.108901i
$616$	−3086.90	−	8373.74i	−0.201907	−	0.547707i
$617$	10889.8	−	6287.22i	0.710545	−	0.410233i	−0.100718	−	0.994915i	$-0.532114\pi$
$617$	10889.8	−	6287.22i	0.710545	−	0.410233i	0.811263	+	0.584682i	$0.198781\pi$
$618$	18516.5	−	8075.09i	1.20525	−	0.525611i
$619$	−604.640	+	1047.27i	−0.0392610	+	0.0680020i	−0.884988	−	0.465613i	$-0.845834\pi$
$619$	−604.640	+	1047.27i	−0.0392610	+	0.0680020i	0.845727	+	0.533616i	$0.179167\pi$
$620$	19345.3	+	14319.7i	1.25311	+	0.927567i
$621$	8638.17	+	23164.9i	0.558193	+	1.49690i
$622$	−7032.18	−	13954.4i	−0.453319	−	0.899552i
$623$	10842.7	−	18780.1i	0.697276	−	1.20772i
$624$	−6677.53	+	1639.92i	−0.428390	+	0.105207i
$625$	7086.90	+	12274.9i	0.453561	+	0.785591i
$626$	−4720.77	+	7199.08i	−0.301406	+	0.459638i
$627$	−12020.3	−	7860.80i	−0.765618	−	0.500686i
$628$	1310.61	−	569.613i	0.0832786	−	0.0361944i
$629$	8098.76			0.513385
$630$	−2444.97	+	14423.3i	−0.154619	+	0.912122i
$631$			9244.14i			0.583207i	0.956539	+	0.291603i	$0.0941888\pi$
$631$			9244.14i			0.583207i	−0.956539	+	0.291603i	$0.905811\pi$
$632$	11303.5	+	9405.72i	0.711438	+	0.591993i
$633$	345.463	+	683.402i	0.0216918	+	0.0429112i
$634$	−10035.4	+	15303.8i	−0.628638	+	0.958661i
$635$	2463.58	−	1422.35i	0.153960	−	0.0888886i
$636$	6475.28	+	1105.98i	0.403713	+	0.0689541i
$637$	−393.378	−	227.117i	−0.0244681	−	0.0141267i
$638$	8599.13	−	4333.43i	0.533609	−	0.268906i
$639$	−546.867	−	61.0159i	−0.0338556	−	0.00377739i
$640$	1945.09	+	15360.1i	0.120135	+	0.948689i
$641$	13346.5	+	7705.58i	0.822392	+	0.474808i	0.851241	−	0.524776i	$-0.175851\pi$
$641$	13346.5	+	7705.58i	0.822392	+	0.474808i	−0.0288488	+	0.999584i	$0.509184\pi$
$642$	2657.61	−	23552.6i	0.163376	−	1.44789i
$643$	2947.93	+	5105.96i	0.180801	+	0.313156i	0.942154	−	0.335182i	$-0.108798\pi$
$643$	2947.93	+	5105.96i	0.180801	+	0.313156i	−0.761353	+	0.648338i	$0.775464\pi$
$644$	2863.54	−	25096.4i	0.175216	−	1.53562i
$645$	−17463.9	−	971.240i	−1.06611	−	0.0592908i
$646$	730.133	−	12839.5i	0.0444686	−	0.781984i
$647$	30355.3			1.84450			0.922249	−	0.386596i	$-0.126349\pi$
$647$	30355.3			1.84450			0.922249	+	0.386596i	$0.126349\pi$
$648$	15240.1	+	6311.67i	0.923901	+	0.382632i
$649$	10268.5			0.621066
$650$	35.5089	−	624.428i	0.00214273	−	0.0376801i
$651$	−26158.4	−	1454.78i	−1.57485	−	0.0875841i
$652$	17732.5	+	2023.30i	1.06512	+	0.121532i
$653$	3997.18	+	6923.31i	0.239543	+	0.414901i	0.960583	−	0.277993i	$-0.0896691\pi$
$653$	3997.18	+	6923.31i	0.239543	+	0.414901i	−0.721040	+	0.692893i	$0.756336\pi$
$654$	−2548.74	+	22587.8i	−0.152391	+	1.35054i
$655$	3036.74	+	1753.26i	0.181153	+	0.104589i
$656$	3343.58	−	1021.04i	0.199001	−	0.0607694i
$657$	−9940.11	−	1109.05i	−0.590260	−	0.0658574i
$658$	−20842.2	+	10503.2i	−1.23482	+	0.622276i
$659$	7708.70	+	4450.62i	0.455673	+	0.263083i	0.710223	−	0.703977i	$-0.248594\pi$
$659$	7708.70	+	4450.62i	0.455673	+	0.263083i	−0.254550	+	0.967060i	$0.581927\pi$
$660$	−1647.13	+	9643.64i	−0.0971432	+	0.568755i
$661$	−5648.33	+	3261.07i	−0.332367	+	0.191892i	−0.656892	−	0.753985i	$-0.728129\pi$
$661$	−5648.33	+	3261.07i	−0.332367	+	0.191892i	0.324524	+	0.945877i	$0.394796\pi$
$662$	−10186.3	+	15533.9i	−0.598038	+	0.911996i
$663$	−1755.10	−	3471.97i	−0.102809	−	0.203379i
$664$	10372.7	+	8631.19i	0.606233	+	0.504451i
$665$		−	24053.2i		−	1.40262i
$666$	2854.62	−	16839.9i	0.166087	−	0.979776i
$667$	27253.8			1.58212
$668$	5883.56	+	13537.3i	0.340781	+	0.784094i
$669$	5249.31	+	3432.85i	0.303363	+	0.198388i
$670$	6417.95	−	9787.25i	0.370070	−	0.564350i
$671$	−4858.59	−	8415.32i	−0.279529	−	0.484158i
$672$	−10954.9	−	12806.9i	−0.628862	−	0.735176i
$673$	−13331.6	+	23091.1i	−0.763591	+	1.32258i	0.177397	+	0.984139i	$0.443232\pi$
$673$	−13331.6	+	23091.1i	−0.763591	+	1.32258i	−0.940988	+	0.338440i	$0.890101\pi$
$674$	−15186.8	−	30136.1i	−0.867911	−	1.72226i
$675$	−955.386	+	1156.94i	−0.0544783	+	0.0659711i
$676$	−8422.15	+	11378.0i	−0.479185	+	0.647359i
$677$	4565.23	−	7907.21i	0.259167	−	0.448890i	−0.706852	−	0.707361i	$-0.749885\pi$
$677$	4565.23	−	7907.21i	0.259167	−	0.448890i	0.966019	+	0.258471i	$0.0832187\pi$
$678$	18559.8	−	8093.96i	1.05130	−	0.458476i
$679$	−24662.6	+	14238.9i	−1.39391	+	0.804772i
$680$	−8219.33	+	3029.97i	−0.463525	+	0.170874i
$681$	2317.11	+	1515.31i	0.130385	+	0.0852667i
$682$	−17492.4	−	994.730i	−0.982139	−	0.0558507i
$683$			4081.15i			0.228640i	0.993444	+	0.114320i	$0.0364689\pi$
$683$			4081.15i			0.228640i	−0.993444	+	0.114320i	$0.963531\pi$
$684$	−26439.9	−	6043.77i	−1.47800	−	0.337850i
$685$		−	22138.9i		−	1.23486i
$686$	1050.10	−	18466.0i	0.0584444	−	1.02775i
$687$	−2349.68	+	1187.77i	−0.130489	+	0.0659628i
$688$	13747.1	−	14732.3i	0.761779	−	0.816372i
$689$	−2829.65	+	1633.70i	−0.156460	+	0.0903323i
$690$	−16446.3	+	22276.3i	−0.907390	+	1.22905i
$691$	3245.02	−	5620.54i	0.178649	−	0.309429i	−0.762769	−	0.646671i	$-0.776161\pi$
$691$	3245.02	−	5620.54i	0.178649	−	0.309429i	0.941418	+	0.337242i	$0.109494\pi$
$692$	−14829.8	+	20034.5i	−0.814661	+	1.10057i
$693$	−4269.13	−	9756.03i	−0.234013	−	0.534778i
$694$	−3668.70	+	1848.80i	−0.200666	+	0.101123i
$695$	−9347.10	+	16189.7i	−0.510152	+	0.883610i
$696$	12389.1	−	13310.3i	0.674726	−	0.724892i
$697$	989.007	+	1713.01i	0.0537465	+	0.0930916i
$698$	−7579.85	−	4970.46i	−0.411034	−	0.269534i
$699$	115.975	−	2085.34i	0.00627550	−	0.112840i
$700$	1405.92	−	611.036i	0.0759124	−	0.0329928i
$701$	29971.5			1.61485			0.807424	−	0.589971i	$-0.200861\pi$
$701$	29971.5			1.61485			0.807424	+	0.589971i	$0.200861\pi$
$702$	−7837.93	+	2425.61i	−0.421401	+	0.130411i
$703$			28083.2i			1.50665i
$704$	−7315.50	−	8573.89i	−0.391638	−	0.459007i
$705$	25545.3	+	1420.68i	1.36467	+	0.0758951i
$706$	9508.21	+	6234.97i	0.506864	+	0.332374i
$707$	19751.3	−	11403.4i	1.05067	−	0.606606i
$708$	18185.6	−	6729.73i	0.965334	−	0.357230i
$709$	2923.29	+	1687.77i	0.154847	+	0.0894011i	0.575421	−	0.817857i	$-0.304838\pi$
$709$	2923.29	+	1687.77i	0.154847	+	0.0894011i	−0.420574	+	0.907258i	$0.638171\pi$
$710$	−277.345	−	550.354i	−0.0146599	−	0.0290907i
$711$	14129.3	+	10404.2i	0.745273	+	0.548788i
$712$	4644.44	−	26989.3i	0.244463	−	1.42060i
$713$	−42945.1	−	24794.3i	−2.25569	−	1.30232i
$714$	5663.55	−	7671.22i	0.296853	−	0.402084i
$715$	−2433.07	−	4214.20i	−0.127261	−	0.220422i
$716$	2227.56	−	19522.6i	0.116268	−	1.01899i
$717$	2049.83	+	4055.02i	0.106768	+	0.211210i
$718$	−12490.2	−	710.270i	−0.649204	−	0.0369179i
$719$	−36696.4			−1.90340			−0.951701	−	0.307025i	$-0.900666\pi$
$719$	−36696.4			−1.90340			−0.951701	+	0.307025i	$0.900666\pi$
$720$	3403.15	+	18158.5i	0.176150	+	0.939901i
$721$	−24627.1			−1.27207
$722$	25153.1	+	1430.36i	1.29654	+	0.0737294i
$723$	2728.40	−	4172.10i	0.140346	−	0.214609i
$724$	−2744.75	+	24055.3i	−0.140895	+	1.23482i
$725$	827.004	+	1432.41i	0.0423644	+	0.0733772i
$726$	4972.75	+	11402.7i	0.254210	+	0.582913i
$727$	18148.3	+	10477.9i	0.925834	+	0.534531i	0.885492	−	0.464655i	$-0.153822\pi$
$727$	18148.3	+	10477.9i	0.925834	+	0.534531i	0.0403426	+	0.999186i	$0.487155\pi$
$728$	8261.19	+	1421.62i	0.420577	+	0.0723748i
$729$	18599.5	+	6440.34i	0.944954	+	0.327203i
$730$	−5041.14	−	10003.5i	−0.255591	−	0.507186i
$731$	9873.34	+	5700.37i	0.499560	+	0.288421i
$732$	−14119.9	−	11719.4i	−0.712958	−	0.591753i
$733$	−11601.1	+	6697.91i	−0.584580	+	0.337508i	−0.762952	−	0.646456i	$-0.776251\pi$
$733$	−11601.1	+	6697.91i	−0.584580	+	0.337508i	0.178371	+	0.983963i	$0.442917\pi$
$734$	−2833.79	−	1858.25i	−0.142503	−	0.0934458i
$735$	−667.979	+	1021.43i	−0.0335221	+	0.0512600i
$736$	−7569.32	−	30988.3i	−0.379088	−	1.55196i
$737$			8519.83i			0.425823i
$738$	3910.48	−	1452.66i	0.195050	−	0.0724568i
$739$	5570.50			0.277286			0.138643	−	0.990342i	$-0.455726\pi$
$739$	5570.50			0.277286			0.138643	+	0.990342i	$0.455726\pi$
$740$	17544.2	−	7625.01i	0.871537	−	0.378785i
$741$	12039.4	−	6085.96i	0.596865	−	0.301718i
$742$	−6697.01	−	4391.54i	−0.331341	−	0.217276i
$743$	2503.74	+	4336.60i	0.123625	+	0.214124i	0.921195	−	0.389102i	$-0.127215\pi$
$743$	2503.74	+	4336.60i	0.123625	+	0.214124i	−0.797570	+	0.603227i	$0.793881\pi$
$744$	−31631.3	+	9702.49i	−1.55868	+	0.478105i
$745$	−551.551	+	955.314i	−0.0271238	+	0.0469799i
$746$	−5343.08	+	2692.58i	−0.262231	+	0.132148i
$747$	12965.8	+	9547.45i	0.635064	+	0.467634i
$748$	3793.95	−	5125.47i	0.185455	−	0.250542i
$749$	−14447.8	+	25024.4i	−0.704822	+	1.22079i
$750$	−21187.3	−	2390.72i	−1.03153	−	0.116396i
$751$	14755.0	−	8518.83i	0.716936	−	0.413923i	−0.0966876	−	0.995315i	$-0.530825\pi$
$751$	14755.0	−	8518.83i	0.716936	−	0.413923i	0.813624	+	0.581391i	$0.197491\pi$
$752$	−20108.6	+	21549.7i	−0.975115	+	1.04500i
$753$	−428.798	+	7710.22i	−0.0207520	+	0.373142i
$754$	−513.500	+	9029.95i	−0.0248018	+	0.436142i
$755$			27222.3i			1.31221i
$756$	−13954.6	−	14480.2i	−0.671328	−	0.696613i
$757$		−	19829.1i		−	0.952049i	−0.879432	−	0.476024i	$-0.842077\pi$
$757$		−	19829.1i		−	0.952049i	0.879432	−	0.476024i	$-0.157923\pi$
$758$	−11863.8	−	674.653i	−0.568488	−	0.0323278i
$759$	1119.27	−	20125.6i	0.0535268	−	0.962466i
$760$	−10506.7	−	28501.3i	−0.501472	−	1.36033i
$761$	14809.3	−	8550.18i	0.705438	−	0.407285i	−0.103932	−	0.994584i	$-0.533142\pi$
$761$	14809.3	−	8550.18i	0.705438	−	0.407285i	0.809370	+	0.587300i	$0.199809\pi$
$762$	−438.466	+	3885.82i	−0.0208451	+	0.184736i
$763$	13856.0	−	23999.2i	0.657431	−	1.13870i
$764$	−9298.08	+	12561.3i	−0.440305	+	0.594833i
$765$	−9576.14	+	4190.41i	−0.452583	+	0.198045i
$766$	2647.96	+	5254.52i	0.124902	+	0.247851i
$767$	−4822.43	+	8352.70i	−0.227025	+	0.393218i
$768$	−18575.0	−	10390.1i	−0.872745	−	0.488176i
$769$	−11253.2	−	19491.1i	−0.527699	−	0.914002i	−0.999479	−	0.0322854i	$-0.989721\pi$
$769$	−11253.2	−	19491.1i	−0.527699	−	0.914002i	0.471779	−	0.881717i	$-0.343612\pi$
$770$	6540.32	−	9973.86i	0.306100	−	0.466796i
$771$	−4339.21	+	2193.49i	−0.202688	+	0.102460i
$772$	5148.57	+	11846.2i	0.240027	+	0.552273i
$773$	−5523.17			−0.256992			−0.128496	−	0.991710i	$-0.541015\pi$
$773$	−5523.17			−0.256992			−0.128496	+	0.991710i	$0.541015\pi$
$774$	15333.0	−	18520.5i	0.712057	−	0.860085i
$775$		−	3009.49i		−	0.139489i
$776$	−23003.6	+	27645.0i	−1.06415	+	1.27886i
$777$	−11396.6	+	17427.0i	−0.526193	+	0.804622i
$778$	5260.57	−	8022.27i	0.242417	−	0.369681i
$779$	−5940.02	+	3429.47i	−0.273200	+	0.157732i
$780$	−7070.90	−	5868.83i	−0.324588	−	0.269407i
$781$	388.522	+	224.313i	0.0178008	+	0.0102773i
$782$	16117.5	−	8122.24i	0.737035	−	0.371421i
$783$	13816.0	−	16730.6i	0.630578	−	0.763606i
$784$	−410.636	−	1344.71i	−0.0187061	−	0.0612567i
$785$	1653.93	+	954.899i	0.0751993	+	0.0434163i
$786$	−4418.38	+	1926.87i	−0.200507	+	0.0874415i
$787$	−3299.97	−	5715.72i	−0.149468	−	0.258886i	0.781563	−	0.623826i	$-0.214423\pi$
$787$	−3299.97	−	5715.72i	−0.149468	−	0.258886i	−0.931031	+	0.364940i	$0.881089\pi$
$788$	27579.8	+	3146.91i	1.24682	+	0.142264i
$789$	−4116.71	+	6295.03i	−0.185753	+	0.284042i
$790$	−1115.74	+	19620.4i	−0.0502483	+	0.883621i
$791$	−24684.6			−1.10959
$792$	−9320.17	−	9695.40i	−0.418154	−	0.434989i
$793$	9127.06			0.408716
$794$	−458.019	+	8054.30i	−0.0204716	+	0.359995i
$795$	3960.56	+	7834.87i	0.176688	+	0.349527i
$796$	−1200.42	+	10520.6i	−0.0534521	+	0.468460i
$797$	−9315.82	−	16135.5i	−0.414032	−	0.717124i	0.581294	−	0.813693i	$-0.302546\pi$
$797$	−9315.82	−	16135.5i	−0.414032	−	0.717124i	−0.995326	+	0.0965692i	$0.969213\pi$
$798$	26600.7	+	19638.9i	1.18002	+	0.871188i
$799$	−14442.2	−	8338.23i	−0.639461	−	0.369193i
$800$	1399.00	−	1338.16i	0.0618278	−	0.0591387i
$801$	3623.53	−	32476.6i	0.159839	−	1.43259i
$802$	2286.69	−	1152.35i	0.100681	−	0.0507368i
$803$	7061.95	+	4077.22i	0.310350	+	0.179180i
$804$	5583.72	+	15088.7i	0.244929	+	0.661864i
$805$	29234.4	−	16878.5i	1.27997	−	0.738992i
$806$	9024.21	−	13761.7i	0.394372	−	0.601410i
$807$	−12753.2	−	709.262i	−0.556302	−	0.0309383i
$808$	18422.7	−	22139.9i	0.802116	−	0.963958i
$809$		−	9731.56i		−	0.422921i	−0.977387	−	0.211461i	$-0.932178\pi$
$809$		−	9731.56i		−	0.422921i	0.977387	−	0.211461i	$-0.0678220\pi$
$810$	5337.81	+	21388.8i	0.231545	+	0.927809i
$811$	12468.7			0.539872			0.269936	−	0.962878i	$-0.412997\pi$
$811$	12468.7			0.539872			0.269936	+	0.962878i	$0.412997\pi$
$812$	−20331.2	+	8836.28i	−0.878675	+	0.381888i
$813$	−139.742	+	2512.69i	−0.00602823	+	0.108394i
$814$	−7636.13	+	11645.0i	−0.328804	+	0.501420i
$815$	11925.9	+	20656.3i	0.512572	+	0.887800i
$816$	3360.01	−	11563.8i	0.144147	−	0.496094i
$817$	−19766.6	+	34236.7i	−0.846444	+	1.46608i
$818$	−10038.4	−	19919.9i	−0.429076	−	0.851445i
$819$	9940.81	+	1109.13i	0.424127	+	0.0473214i
$820$	3755.27	+	2779.71i	0.159926	+	0.118380i
$821$	−3801.24	+	6583.94i	−0.161589	+	0.279880i	−0.935439	−	0.353489i	$-0.884995\pi$
$821$	−3801.24	+	6583.94i	−0.161589	+	0.279880i	0.773850	+	0.633369i	$0.218328\pi$
$822$	24483.6	+	18075.9i	1.03889	+	0.766993i
$823$	30246.1	−	17462.6i	1.28106	−	0.739622i	0.304020	−	0.952666i	$-0.401671\pi$
$823$	30246.1	−	17462.6i	1.28106	−	0.739622i	0.977043	+	0.213044i	$0.0683377\pi$
$824$	−29181.3	+	10757.4i	−1.23371	+	0.454796i
$825$	1091.73	−	551.874i	0.0460717	−	0.0232895i
$826$	−23601.7	−	1342.14i	−0.994197	−	0.0565363i
$827$		−	8660.10i		−	0.364137i	−0.983286	−	0.182068i	$-0.941721\pi$
$827$		−	8660.10i		−	0.364137i	0.983286	−	0.182068i	$-0.0582792\pi$
$828$	−11207.6	−	36376.2i	−0.470402	−	1.52677i
$829$		−	15475.5i		−	0.648353i	−0.945997	−	0.324177i	$-0.894913\pi$
$829$		−	15475.5i		−	0.648353i	0.945997	−	0.324177i	$-0.105087\pi$
$830$	−1023.86	+	18004.7i	−0.0428177	+	0.752954i
$831$	17961.5	+	11746.1i	0.749791	+	0.490335i
$832$	10409.9	−	1924.07i	0.433772	−	0.0801743i
$833$	688.932	−	397.755i	0.0286555	−	0.0165443i
$834$	−10272.6	−	23555.6i	−0.426513	−	0.978012i
$835$	−9863.19	+	17083.6i	−0.408778	+	0.708025i
$836$	17773.0	+	13155.9i	0.735278	+	0.544264i
$837$	−36991.3	+	13794.0i	−1.52761	+	0.569643i
$838$	35847.4	−	18064.9i	1.47772	−	0.744679i
$839$	−4487.20	+	7772.06i	−0.184643	+	0.319811i	−0.943456	−	0.331497i	$-0.892446\pi$
$839$	−4487.20	+	7772.06i	−0.184643	+	0.319811i	0.758813	+	0.651308i	$0.225780\pi$
$840$	5046.35	−	21950.3i	0.207280	−	0.901614i
$841$	235.069	+	407.151i	0.00963831	+	0.0166940i
$842$	38229.8	+	25069.1i	1.56471	+	1.02605i
$843$	−3686.98	−	2411.15i	−0.150636	−	0.0985105i
$844$	−469.932	−	1081.25i	−0.0191655	−	0.0440975i
$845$	−18918.3			−0.770189
$846$	−22428.3	+	27090.9i	−0.911467	+	1.10095i
$847$		−	15165.7i		−	0.615230i
$848$	−9853.76	−	2278.32i	−0.399032	−	0.0922617i
$849$	−12689.3	−	25102.3i	−0.512952	−	1.01473i
$850$	915.970	+	600.644i	0.0369618	+	0.0242375i
$851$	−34132.6	+	19706.4i	−1.37491	+	0.793805i
$852$	835.088	+	142.633i	0.0335794	+	0.00573535i
$853$	11129.3	+	6425.49i	0.446728	+	0.257919i	0.706447	−	0.707766i	$-0.250297\pi$
$853$	11129.3	+	6425.49i	0.446728	+	0.257919i	−0.259719	+	0.965684i	$0.583630\pi$
$854$	10067.4	+	19977.3i	0.403393	+	0.800481i
$855$	−14530.6	−	33206.1i	−0.581212	−	1.32822i
$856$	−6188.69	+	35963.1i	−0.247109	+	1.43597i
$857$	−23236.8	−	13415.7i	−0.926199	−	0.534741i	−0.0405914	−	0.999176i	$-0.512924\pi$
$857$	−23236.8	−	13415.7i	−0.926199	−	0.534741i	−0.885607	+	0.464435i	$0.846258\pi$
$858$	6647.08	+	750.039i	0.264484	+	0.0298437i
$859$	−13594.8	−	23546.9i	−0.539987	−	0.935284i	−0.998904	−	0.0468052i	$-0.985096\pi$
$859$	−13594.8	−	23546.9i	−0.539987	−	0.935284i	0.458918	−	0.888479i	$-0.348237\pi$
$860$	26755.3	+	3052.83i	1.06087	+	0.121047i
$861$	−5077.81	−	282.399i	−0.200989	−	0.0111778i
$862$	28113.5	+	1598.71i	1.11085	+	0.0631698i
$863$	−10963.4			−0.432441			−0.216221	−	0.976345i	$-0.569373\pi$
$863$	−10963.4			−0.432441			−0.216221	+	0.976345i	$0.569373\pi$
$864$	−22860.3	−	11062.5i	−0.900144	−	0.435593i
$865$	−33311.6			−1.30940
$866$	−10690.3	−	607.917i	−0.419480	−	0.0238543i
$867$	−18686.5	−	1039.24i	−0.731982	−	0.0407086i
$868$	40075.6	+	4572.70i	1.56712	+	0.178810i
$869$	−7152.86	−	12389.1i	−0.279222	−	0.483627i
$870$	24148.1	+	2724.81i	0.941032	+	0.106184i
$871$	−6930.31	−	4001.21i	−0.269603	−	0.155656i
$872$	5935.17	−	34489.9i	0.230494	−	1.33942i
$873$	−25445.6	+	34556.1i	−0.986488	+	1.33969i
$874$	28164.6	+	55889.0i	1.09003	+	2.16301i
$875$	22511.3	+	12996.9i	0.869737	+	0.502143i
$876$	15179.0	+	2592.56i	0.585444	+	0.0999938i
$877$	23926.8	−	13814.2i	0.921268	−	0.531894i	0.0372287	−	0.999307i	$-0.488147\pi$
$877$	23926.8	−	13814.2i	0.921268	−	0.531894i	0.884039	+	0.467412i	$0.154814\pi$
$878$	37222.9	+	24408.8i	1.43077	+	0.938219i
$879$	19498.0	+	38571.3i	0.748181	+	1.48007i
$880$	3393.11	−	14675.2i	0.129979	−	0.562160i
$881$			3160.30i			0.120855i	0.998173	+	0.0604275i	$0.0192464\pi$
$881$			3160.30i			0.120855i	−0.998173	+	0.0604275i	$0.980754\pi$
$882$	−584.225	−	1572.70i	−0.0223037	−	0.0600404i
$883$	25009.6			0.953161			0.476581	−	0.879131i	$-0.341876\pi$
$883$	25009.6			0.953161			0.476581	+	0.879131i	$0.341876\pi$
$884$	2387.45	+	5493.22i	0.0908356	+	0.209001i
$885$	21688.4	+	14183.4i	0.823781	+	0.538722i
$886$	14070.7	+	9226.82i	0.533538	+	0.349866i
$887$	482.657	+	835.987i	0.0182706	+	0.0316457i	0.875016	−	0.484094i	$-0.160851\pi$
$887$	482.657	+	835.987i	0.0182706	+	0.0316457i	−0.856746	+	0.515739i	$0.827517\pi$
$888$	−5891.85	+	25628.0i	−0.222655	+	0.968489i
$889$	2383.67	−	4128.64i	0.0899279	−	0.155760i
$890$	32683.6	−	16470.6i	1.23096	−	0.620331i
$891$	−11787.3	−	10889.5i	−0.443199	−	0.409441i
$892$	−7761.57	−	5745.23i	−0.291341	−	0.215655i
$893$	28913.6	−	50079.8i	1.08349	−	1.87666i
$894$	−606.164	−	1389.96i	−0.0226769	−	0.0519991i
$895$	22741.6	−	13129.9i	0.849348	−	0.490372i
$896$	15693.8	+	20662.9i	0.585147	+	0.770424i
$897$	15845.1	+	10362.1i	0.589804	+	0.385710i
$898$	−2427.47	+	42687.3i	−0.0902069	+	1.58630i
$899$			43520.7i			1.61457i
$900$	1571.78	−	1692.88i	0.0582142	−	0.0626991i
$901$		−	5722.27i		−	0.211583i
$902$	−3395.59	−	193.095i	−0.125345	−	0.00712790i
$903$	−26160.0	+	13224.0i	−0.964063	+	0.487338i
$904$	−29249.5	+	10782.5i	−1.07613	+	0.396706i
$905$	−28021.6	+	16178.3i	−1.02925	+	0.594237i
$906$	−30105.5	−	22226.4i	−1.10396	−	0.815036i
$907$	14900.6	−	25808.6i	0.545498	−	0.944830i	−0.453078	−	0.891471i	$-0.649674\pi$
$907$	14900.6	−	25808.6i	0.545498	−	0.944830i	0.998575	−	0.0533589i	$-0.0169927\pi$
$908$	−3426.06	−	2536.02i	−0.125218	−	0.0926881i
$909$	20378.4	−	27674.6i	0.743576	−	1.00980i
$910$	5041.50	+	10004.2i	0.183653	+	0.364435i
$911$	−4525.83	+	7838.97i	−0.164597	+	0.285090i	−0.936512	−	0.350636i	$-0.885966\pi$
$911$	−4525.83	+	7838.97i	−0.164597	+	0.285090i	0.771915	+	0.635725i	$0.219299\pi$
$912$	40098.4	+	11651.2i	1.45591	+	0.423035i
$913$	−6563.84	−	11368.9i	−0.237932	−	0.412110i
$914$	5514.97	−	8410.23i	0.199583	−	0.304361i
$915$	1361.73	−	24485.2i	0.0491993	−	0.884653i
$916$	3717.58	−	1615.72i	0.134096	−	0.0582806i
$917$	5876.48			0.211623
$918$	3184.48	−	14011.7i	0.114492	−	0.503765i
$919$			25649.5i			0.920674i	0.887744	+	0.460337i	$0.152271\pi$
$919$			25649.5i			0.920674i	−0.887744	+	0.460337i	$0.847729\pi$
$920$	27268.0	−	32769.8i	0.977171	−	1.17433i
$921$	40462.3	+	2250.28i	1.44764	+	0.0805096i
$922$	13725.7	−	20931.4i	0.490273	−	0.747657i
$923$	−364.927	+	210.691i	−0.0130138	+	0.00751351i
$924$	5690.19	+	15376.4i	0.202590	+	0.547455i
$925$	−2071.47	−	1195.97i	−0.0736320	−	0.0425115i
$926$	−33331.5	+	16797.0i	−1.18287	+	0.596096i
$927$	−33998.4	+	14877.3i	−1.20459	+	0.527115i
$928$	−20231.2	+	19351.3i	−0.715648	+	0.684522i
$929$	48149.3	+	27799.0i	1.70046	+	0.981762i	0.945288	+	0.326237i	$0.105781\pi$
$929$	48149.3	+	27799.0i	1.70046	+	0.981762i	0.755174	+	0.655525i	$0.227553\pi$
$930$	−35572.4	−	26262.5i	−1.25426	−	0.926002i
$931$	1379.25	+	2388.93i	0.0485533	+	0.0840968i
$932$	−364.535	+	3194.83i	−0.0128120	+	0.112285i
$933$	12950.9	+	25619.8i	0.454442	+	0.898986i
$934$	1431.95	−	25181.1i	0.0501659	−	0.882173i
$935$	8522.18			0.298080
$936$	12263.6	−	3028.03i	0.428258	−	0.105742i
$937$	−24617.9			−0.858304			−0.429152	−	0.903232i	$-0.641187\pi$
$937$	−24617.9			−0.858304			−0.429152	+	0.903232i	$0.641187\pi$
$938$	1113.59	−	19582.5i	0.0387632	−	0.681654i
$939$	8656.09	−	13236.4i	0.300832	−	0.460014i
$940$	−39136.4	−	4465.53i	−1.35797	−	0.154946i
$941$	5553.99	+	9619.80i	0.192407	+	0.333259i	0.946047	−	0.324028i	$-0.105037\pi$
$941$	5553.99	+	9619.80i	0.192407	+	0.333259i	−0.753640	+	0.657287i	$0.771704\pi$
$942$	−2406.43	+	1049.45i	−0.0832334	+	0.0362983i
$943$	−8336.41	−	4813.03i	−0.287880	−	0.166208i
$944$	−28552.5	+	8719.15i	−0.984434	+	0.300619i
$945$	4458.62	−	26502.8i	0.153480	−	0.912314i
$946$	−17505.7	+	8821.81i	−0.601649	+	0.303194i
$947$	17487.0	+	10096.1i	0.600055	+	0.346442i	0.769063	−	0.639173i	$-0.220723\pi$
$947$	17487.0	+	10096.1i	0.600055	+	0.346442i	−0.169008	+	0.985615i	$0.554057\pi$
$948$	−20787.4	−	17253.5i	−0.712176	−	0.591104i
$949$	−6633.09	+	3829.61i	−0.226891	+	0.130995i
$950$	−2082.79	+	3176.21i	−0.0711311	+	0.108474i
$951$	18401.1	−	28137.9i	0.627441	−	0.959445i
$952$	−9390.17	+	11284.8i	−0.319682	+	0.384183i
$953$		−	18808.4i		−	0.639310i	−0.947534	−	0.319655i	$-0.896433\pi$
$953$		−	18808.4i		−	0.639310i	0.947534	−	0.319655i	$-0.103567\pi$
$954$	−11898.4	−	2016.96i	−0.403799	−	0.0684502i
$955$	−20885.9			−0.707697
$956$	−2788.37	−	6415.70i	−0.0943331	−	0.217049i
$957$	−15787.7	+	7980.74i	−0.533273	+	0.269572i
$958$	−10089.1	+	15385.6i	−0.340253	+	0.518880i
$959$	−18550.9	−	32131.1i	−0.624651	−	1.08193i
$960$	−3608.58	−	28213.8i	−0.121319	−	0.948538i
$961$	24697.8	−	42777.8i	0.829035	−	1.43593i
$962$	−5886.19	−	11680.4i	−0.197275	−	0.391466i
$963$	−4828.34	+	43274.9i	−0.161569	+	1.44809i
$964$	−4566.26	+	6168.82i	−0.152561	+	0.206104i
$965$	−8631.06	+	14949.4i	−0.287921	+	0.498694i
$966$	−5203.11	+	46111.6i	−0.173300	+	1.53583i
$967$	−590.535	+	340.946i	−0.0196384	+	0.0113382i	−0.509787	−	0.860301i	$-0.670276\pi$
$967$	−590.535	+	340.946i	−0.0196384	+	0.0113382i	0.490149	+	0.871639i	$0.336942\pi$
$968$	−6624.57	−	17970.3i	−0.219960	−	0.596680i
$969$	−1311.90	+	23589.2i	−0.0434925	+	0.782039i
$970$	−47985.6	−	2728.77i	−1.58838	−	0.0903252i
$971$		−	54483.2i		−	1.80067i	−0.435197	−	0.900335i	$-0.643321\pi$
$971$		−	54483.2i		−	1.80067i	0.435197	−	0.900335i	$-0.356679\pi$
$972$	−28012.3	−	11560.3i	−0.924378	−	0.381479i
$973$			31329.1i			1.03223i
$974$	3348.25	−	58879.3i	0.110149	−	1.93697i
$975$	−63.8022	+	1147.23i	−0.00209570	+	0.0376828i
$976$	20655.4	+	19274.2i	0.677423	+	0.632122i
$977$	−26948.6	+	15558.8i	−0.882458	+	0.509487i	−0.871468	−	0.490452i	$-0.836832\pi$
$977$	−26948.6	+	15558.8i	−0.882458	+	0.509487i	−0.0109896	+	0.999940i	$0.503498\pi$
$978$	−32581.2	−	3676.38i	−1.06527	−	0.120202i
$979$	−13321.2	+	23073.0i	−0.434880	+	0.753234i
$980$	1117.93	−	1510.28i	0.0364398	−	0.0492287i
$981$	4630.55	−	41502.2i	0.150705	−	1.35073i
$982$	−9672.50	+	4874.35i	−0.314320	+	0.158398i
$983$	5791.66	−	10031.4i	0.187920	−	0.325487i	−0.756637	−	0.653836i	$-0.773159\pi$
$983$	5791.66	−	10031.4i	0.187920	−	0.325487i	0.944557	+	0.328349i	$0.106492\pi$
$984$	−6140.20	+	1883.43i	−0.198925	+	0.0610178i
$985$	18548.7	+	32127.3i	0.600011	+	1.03925i
$986$	−13246.0	−	8686.00i	−0.427828	−	0.280546i
$987$	38265.5	−	19343.4i	1.23405	−	0.623817i
$988$	−19048.2	+	8278.70i	−0.613366	+	0.266580i
$989$	−55482.1			−1.78385
$990$	3003.86	−	17720.3i	0.0964332	−	0.568876i
$991$			23086.5i			0.740028i	0.929026	+	0.370014i	$0.120647\pi$
$991$			23086.5i			0.740028i	−0.929026	+	0.370014i	$0.879353\pi$
$992$	49484.2	−	12087.2i	1.58379	−	0.386864i
$993$	18677.8	−	28560.9i	0.596899	−	0.912742i
$994$	−863.684	−	566.357i	−0.0275597	−	0.0180722i
$995$	−12255.3	+	7075.61i	−0.390472	+	0.225439i
$996$	−19075.6	−	15832.7i	−0.606862	−	0.503694i
$997$	−39030.9	−	22534.5i	−1.23984	−	0.715822i	−0.270779	−	0.962642i	$-0.587281\pi$
$997$	−39030.9	−	22534.5i	−1.23984	−	0.715822i	−0.969062	+	0.246819i	$0.920615\pi$
$998$	4162.02	+	8258.97i	0.132010	+	0.261957i
$999$	−5205.65	+	30943.3i	−0.164864	+	0.979983i

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.4.l.b.11.31	yes	64
3.2	odd	2		216.4.l.b.35.2		64
4.3	odd	2		288.4.p.b.47.32		64
8.3	odd	2	inner	72.4.l.b.11.23	✓	64
8.5	even	2		288.4.p.b.47.31		64
9.4	even	3		216.4.l.b.179.10		64
9.5	odd	6	inner	72.4.l.b.59.23	yes	64
12.11	even	2		864.4.p.b.143.8		64
24.5	odd	2		864.4.p.b.143.25		64
24.11	even	2		216.4.l.b.35.10		64
36.23	even	6		288.4.p.b.239.31		64
36.31	odd	6		864.4.p.b.719.25		64
72.5	odd	6		288.4.p.b.239.32		64
72.13	even	6		864.4.p.b.719.8		64
72.59	even	6	inner	72.4.l.b.59.31	yes	64
72.67	odd	6		216.4.l.b.179.2		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.l.b.11.23	✓	64	8.3	odd	2	inner
72.4.l.b.11.31	yes	64	1.1	even	1	trivial
72.4.l.b.59.23	yes	64	9.5	odd	6	inner
72.4.l.b.59.31	yes	64	72.59	even	6	inner
216.4.l.b.35.2		64	3.2	odd	2
216.4.l.b.35.10		64	24.11	even	2
216.4.l.b.179.2		64	72.67	odd	6
216.4.l.b.179.10		64	9.4	even	3
288.4.p.b.47.31		64	8.5	even	2
288.4.p.b.47.32		64	4.3	odd	2
288.4.p.b.239.31		64	36.23	even	6
288.4.p.b.239.32		64	72.5	odd	6
864.4.p.b.143.8		64	12.11	even	2
864.4.p.b.143.25		64	24.5	odd	2
864.4.p.b.719.8		64	72.13	even	6
864.4.p.b.719.25		64	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	72.4.l.b.11.31

Level	$72$
Weight	$4$
Character	72.11
Analytic conductor	$4.248$
Analytic rank	$0$
Dimension	$64$
Inner twists	$4$